Which is better for an improving amateur to play even better: correspondence chess or faster time controls[both online]? Currently, I do the following in order to improve my chess:

Play several (currently 9) correspondence chess games simultaneously on Chess.com.

Do tactics and puzzles regularly on Lichess.com and Chess.com.

Play occasionally against the computer (though not full strength) in rapid time controls (10|15).


I chose to play correspondence chess as it provides me a  considerably good amount of time to think, and hence play to my best.
I also find that correspondence chess is easier to manage, as I don't have to be online throughout the game.
The thing is, correspondence chess moves so slowly, I feel that it would take me years to complete two dozen games (and hence improve my game).
My questions
So is it a good idea

to play faster time controls too (online),

or to increase the number of simultaneous correspondence chess games I play?


If the second course of action is better, how many games should I (optimally) play simultaneously to increase my performance?
If the first is better, what time control is the most suited to my need?
Note
Information that could be of some use to potential answerers.

I've heard that Blitz and Bullet chess aren't really good for learners.

My rating was between 1200 and 1300 in the rapid time control on Chess.com (before my data got erased).

My training (puzzles) reading online Lichess reached 1903 before falling to 1842, after which I've been inactive for quite a while.
Correspondence chess will do more to improve the quality of your game. That is, your moves will be a lot more thoughtful and deliberate, and so will your opponent's. When you lose, it will probably be due to a subtle mistake beyond your ordinary comprehension (have better players point out where and why you lost).

That said, "fast" games may do more to improve your playing strength. There will be times when you will "under the gun" and make "stupid" mistakes under time pressure. In the short run, at least, minimizing such mistakes will do more to improve your rating.