I've started reading about the 1960 Tal vs Botvinnik match and I'm planning on studying many annotated games like these. I was curious about what benefits I can get out of doing this. I've already noticed that I've become more able to read the moves and keep the position in my head. This has strengthened my calculation, but are there any other benefits? Will I start playing more accurately and like the players whose games I study?
Tal vs Botvinnik 1960 is very good as Tal is quite verbose in commentary and what he was thinking about during the game. In addition to the benefits you mentioned, the annotations help you understand what strong players think about in different positions and how they approach the game. Particularly useful is the strong player's positional understanding and ideas in the middlegame. If you happen to play the same openings as those in the annotated games, then you also may get some insights in typical motifs of the opening.
Playing over many GM games is excellent. You get used to seeing good moves which improves your intuition at playing.
Annotation is helpful but only when you have a real question about what was done.
In general things that happen and are explained are rare and not that useful. Far better to study tactics than obsess about annotations.
I would suggest you play over all GM games in a tournament book but especially those that use the opening you have decided to focus on. NOTE: you should select ONE opening for white and black and master that opening not spread yourself too thin trying to learn several openings.
Playing through annotated game collections can be very useful. However in this regard I very much agree with Dan Heisman who advocates strongly for what he calls Instructive Game Anthologies. He distinguishes this from game collection books by a top grandmaster and says that the author of an instructive anthology is trying to use the game to demonstrate and highlight key ideas in order to help instruct the reader. Whereas game collections are often not trying to provide instruction and may contain deep analysis of sidelines that are hard to follow unless you are a very strong player.
Dan has a great list on his website where he puts in order a set of instructive game anthologies: https://www.danheisman.com/recommended-book-lists.html