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He was seen as an enemy of Rome and was to stand trial for crimes

Only by the patricians. Caesar had the support of the plebians the entire time (which is the reason why Brutus was chased out of Rome after Caesar's assassination).
Not to mention that despite being seen as "an enemy of Rome" he had command of the massive army he used to conquer Gaul. It's not like he was ever really at the bottom.

Being able to persuade, encourage, and change people to your favor in public orating seems like a different task than writing papers or reading books.

Being an effective writer requires an understanding in and skill with rhetoric though. A huge part of rhetoric is communication - an essential skill for both persuading people in both written and spoken formats.
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I'd probably caveat your statements by noting that Caesar was an avid self-promoter and built up a cult of personality around himself. Without a doubt, he was a brilliant, brilliant man ... but given that he was the first in a long line of dictators using his name for legitimacy, I think it's rational to bear that in mind when reading glowing Roman accounts of how brilliant he was.
Powerful men with a desire and incentive toward self-aggrandizing can often be successful in building a tremendous amount of personal mythology. e.g., a few years ago Elon Musk had millions of people willing to claim he was a genius, an accomplished engineer, a marvelous rhetorician, etc.
With all that said, some rebuttals for Caesar, specifically:

Engineering. Caesar's decision to build a bridge across the Rhine was certainly militarily intelligent, but his bridge wasn't novel; the design had existed for 500 years by this point, and was the same design as was employed for the Pons Sublicius, the oldest bridge in Rome. Additionally, it's worth noting that Caesar was accompanied on his Gallic campaigns by a quite famous chief engineer (praefector fabrum) named Lucius Balbus. Which of the two seems more likely to have come up with novel engineering concepts?
Literacy and Rhetoric. These weren't particularly different skills in ancient Rome. No disagreement that Caesar was a phenomenal communicator ... but then again, most truly memorable politicians are, aren't they? One note, though ... reading silently was an unusual way to read, and was more odd / impolite than a sign of genius. It indicated that you were concentrating on the message so hard you forgot to read it aloud.
Explorer. What you're highlighting is also an extension of literacy / rhetoric. Caesar didn't explore places other Romans had never been ... instead, he provided lots of gripping details about his campaigns to ensure Romans believed his (self aggrandising) accounts. That didn't require him to be particularly truthful about the people he encountered, and much of his writing is out of line with historians of the era (e.g., Livy disagrees with him about population counts, territorial dispositions, etc ... and is more in-line with archaeological evidence). Even Caesar's friends and subordinates questioned the accuracy of Commentarii de Bello Gallico.
Furthermore, in no circumstance did Caesar travel / explore farther than other Romans, and Romans themselves didn't explore so far as, say, the Phoenicians. We can certainly wonder if Caesar made it to Denmark in the 50s BCE... but we know the Phoenicians did, 800 years earlier.
The Caesar Cypher. This is named after Caesar because he's famous, not because he invented it. Suetonius (our source for him using it) didn't say he'd come up with it, either -- just that he used it. It'd have been odd if he invented it, because transposition ciphers were 1,500 years old by that point, and both the Hebrews (in around 500 BCE) and the Greeks (in around 300 BCE) were using similar, but more secure, cyphers.

To boil it down... what you've described is a man with an incredible military mind, extremely literate, and a consummate politician ... but not someone exceptional as a scientist, artist, musician, explorer, astronomer, philosopher, etc. ie, you've described someone who isn't really a polymath at all.
Compare Caesar to say, Benjamin Franklin. Ben certainly wasn't as skilled of a military strategist, but one could easily argue that he was:

Just as good a communicator and writer
Accomplished (in his own right, not for an employee's work) in engineering, practical philosophy (see: numerous list of inventions), mathematics, statistics, chemistry, business, and political philosophy.
A talented musician, a serviceable composer, and a habitual illustrator >

I agree with most things here. But come on… you can say Elon Musk is accomplished / intelligent while also disagreeing with him or thinking him the devil himself. Not everyone who is your ideological enemy has the capacity of a toad. >

That's not the point -- I think Musk is great at hiring intelligent people, had sound business sense for most of his career, and is an incredible promoter and salesman. What he isn't is an engineer or inventor... By inclination, education, or professional experience. 
And yet, you get articles like this from a few years ago, which work on the fallacy that being an accomplished executive in several fields requires you, yourself, to possess all the individual skills necessary to succeed in those fields.
You don't -- any more than Caesar needed to be an accomplished engineer to benefit from accomplished engineering. >

Yeah very true, I agree with this take. >

This certainly isn’t enough to change your view, but as something to consider, it shouldn’t be seen as impressive that Caesar could read silently. It was just as easy for ancient Romans to read as it would be for any of us. If people didn’t read silently, it was a matter of custom not ability. >


It was just as easy for ancient Romans to read as it would be for any of us

This isn't true. For two reasons. First have you ever actually tried to read Latin from the late Republic? Dear god is it bad. The punctuation was non existent, there weren't even clearly defined sentences and words allrantogetherlikethis.
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The second reason is they were surrounded much less by the written word than we are today. Your average person is exposed to thousands of words a day and has to read constantly just to functionally operate in modern society. Even for Roman aristocrats they didn't have to read particularly often and literature was very expensive and hard to come by. >

That’s just wrong. Plenty of languages are written without spaces and punctuation Nan’s wealthy classes would be exposed enough to the written word to be passable readers >

sureplentyoflanguagesarewrittenwithneitherspacesnorpunctuationbutitshardtoargueitdoesntmakeiteasiertoreadwhenyouhavethemespeciallyinthelatinalphabet
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And it's also seriously hard to argue that Romans would have been exposed to the written world as much as we are today. Most business was conducted in person, public announcements were spoken not written, books were incredibly expensive and few people could afford to own one. You're talking about a society where relatively large numbers of people could read but that reading was just inevitably going to be at a lower level. >

I personally consider the subjects of literacy and rhetoric to be heavily overlapping fields.
Basically the only two discrete fields you have here are engineering and literacy. Which hardly fits the definition of "many" required to be a renaissance man.

He once talked his way out of captivity from criminal pirates (who could have easily killed him) and defused an army about to rebel on him purely by his words and charisma

Minor correction - he didn't talk his way out of captivity. Caesar had a ransom paid. In fact, he told the pirates they were idiots for only asking for 20 talents instead of 50. Then once he was released he gathered a naval force, captured the men, and had them crucified like he promised.
Additionally, politically much of his influence came from the fact that he was a member of the Triumvirate that plundered Rome of its wealth and political stability along with Crassus and Pompey. >

What influence did he have after the Civil War started? He was seen as an enemy of Rome and was to stand trial for crimes. By the end of his life, only a handful of hundreds of senators betrayed him and all of them were swiftly executed afterwards. Caesar was at the bottom before he personally fought his way back to the top.
"literacy and rhetoric to be heavily overlapping fields" Thats up to you, but how often does it translate to real world applications? Being able to persuade, encourage, and change people to your favor in public orating seems like a different task than writing papers or reading books.