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The SNP would have a golden opportunity to force our overlords at Westmisnter to respect teh democratic voice of the people of Scotland.
Of course both sides of the Westminster rulers know that having Scotland under their thumb is a huge benefit to them so they'd be really reluctant to risk losing a referendum and they'd try to offer anything they could short of that. 
What should keep everyone awake at night is both the red and the blue tories have said they'd rahter lose than respect democracy in Scotland so in theory they'd both rather work together than with the SNP.  That makes sense I suppose since they are both right wing neo-liberal parties these days.
But the hope would be that they'd go back on their word (as they often do) and trade treating Scoltand with basic respect for the votes to do whatever crooked shit they'd prefer to do in Westminster.  The SNP could hold there nose for one election cycle, get free of the lot of them and then focus on the future of Scotland.
Ideally the English would feel the same disgust at this arrangement as we do up in Scotland and find an alternative party to elect to challenge those bastards.  Surely there is some group that would put the people first.
In the scenario you describes above, I think it is more likely that Labour would agree to attempt to turn the UK into a federal country rather than give SNP the referendum they want especially considering the polling on Scottish independence is still neck-and-neck and Labour definitely do not want to be held responsible for any potential breakup of the UK. On the other hand, I could also see Labour agreeing to the independence referendum and then working with the Tories to threaten Scotland with partition of its territory in the event the Yes side wins pointing to France's decision to partition Comoros and Canada's threat to partition Quebec as legal precedents.
However, I highly doubt the scenario you are proposing will actually happen. Most of the recent polls show that Labour will win at least a comfortable majority in the next general election. Sure, a lot could change in the next 2 years but Keir Starmer has been working hard to repair Labour's image among voters by moving to the center and presenting himself as a viable alternative to the Tories. Starmer has purged Jeremy Corbyn and much of the far-left from the party while keeping MPs who still support Corbyn's reinstatement on the backbench.   The Labour Party Conference last September featured a tribute to the late Queen and an uninterrupted singing of God Save the King with the national flag on the background. Also, the Labour's position on immigration and asylum seekers is no longer different from that of the Tories. With all this, I am sure Labour is still very much on their way to a historic landslide victory. >

Not sure the party has been making themselves a more appropriate choice vs the Tories with what is shown in the Labour conference last year (constantly having to reaffirm that anti-semitism is not allowed and being boo’d for it, female MPs being threatened into not showing up as seen with Rosie Duffield, claiming that capitalism won’t solve climate change but socialism will by some speaker). >

Well the last point is accurate >

The reality is "Labour will GE tin bed with the SNP and give them endless referendums" was one of the stronger attack points in 2019.
In the run up to the election Labour has to, and has by the way, said that under no circumstances will they form a coalition with the SNP.
There's basically two outcomes to the election that matter for your question.
Scenario 1 is that both Labour and Tories could theoretically form a government but they need the support of other parties to do so.
Scenario 2 is that only Labour can form a government, but requires other parties.
In scenario 1 the incumbent party actually gets first crack at forming a coalition. The Lib Dems won't be keen to form a second LibTory coalition considering the last one killed the party. The reality is the most likely outcome is that any majority the Tories could form would be very weak. This would mean though that they could form a government and lock out Labour and the SNP even if they wanted to work together. So let's assume that happens but if falls apart, and then Labour has a chance. Well forming a coalition with the SNP would be going back on a clear election promise, not a wise idea when the next election may be around the corner. Most likely outcome is Labour say they will form a minority government which the SNP will vote for and basically they will have to negotiate every piece of legislation. This helps Labour if they are smart because smart plays mean anything the SNP blocks they look like the bad guys but if they just vote for everything and get nothing in return people will think why bother voting SNP. 
The second scenario is basically just the latter half of the above. Labour form a minority government and basically blame the SNP for anything that can't get done. 
The goal in both of these scenarios is to way h the Tories implode, formulate a message of "we could do so much more if we didn't have to rely on the SNP" and then head into another election aiming for a majority. 
There's basically 0 chance Labour will agree to another referendum. It would lose the blue vote they've only just regained. >

I think now that Brexit is a more than a half decade old and all the nahnahnah-you-can't-regulate-us-anymore has been replaced by economic woes, I think there's just going to be a shift to Labour, who, instead of giving Scotland another referendum, might instead have a referendum about rejoining the EU. The SNP will back that.
As for first-past the post, it sucks when a smaller group gets more power, but the UK situation is better than giving a bunch of land 40% of your senate. >

Rejoining the EU is pretty damn near a non-starter. For one thing, a major reason Labour didn't already go hard against Brexit is that they have enough Euroskeptic voters that it was as likely to hurt them as to help. 
For another, the UK could never rejoin on their old terms, which were effectively a sweetheart deal. The EU honoured old opt-outs for the UK that allowed them to, for example, keep the pound. Those deals are void now and they have no reason whatsoever to offer them again. Especially since Brexit was arguably beneficial to the EU—it simultaneously removed the major country most likely to oppose further EU reforms and served as proof that leaving the EU is an immensely stupid decision. They have no reason whatsoever to let the UK back in with any concessions at all. >

This is very common elsewhere and generally it means that the spoiler party gets to push through one or two pet agendas that somewhat align with the ruling party and little more. In the Westminster system they could pull down the ruling party essentially at any time but there's no profit in it for them as the move is universally unpopular and they'd lose seats and therefore influence in the process. It's even been speculated at times that the party in charge might incentivise the third rank party to do so just to go from minority to majority, although that again is merely a fanciful situation.