Chess can be broken into three general stages of the game (common terms) called the:
Opening: mostly "book moves", choosing a setup and "opening principles"
https://www.chess.com/blog/KeSetoKaiba/opening-principles-again
Middlegame: What you are asking about which is probably the most complicated stage of the game because middlegame positions can be so different from another so there aren't really any "catch all" generalizations that apply.
Endgame: most pieces exchanged off of the chess board and when checkmate is more likely or the plan of advancing pawns towards promotion is more commonplace.
Obviously, this is opinionated as a stage doesn't transfer instantly by definition - it is a guideline. A grandmaster might call an "endgame" a position they have well studied with many pieces on the board still and someone else might call moves past 40 "endgame" - it is opinionated for these guideline stages of the game.
As soon as the "opening" stage ends (book moves run out) you usually need to reconsider the position slightly differently. In the middlegame, you might do many things. You might try improving your worst pieces by relocating them to more active squares, you might try to provoke tactics to win material, you might embark positional concepts like getting a Rook to an open file and so many more things. The middlegame isn't always so obvious on what to do...even for experienced players!
If in complete doubt, then I recommend usually trying to improve your pieces. Try to get everything you have working together towards a common goal (targeting a weakness, attacking the enemy King etc. as every position is unique) and usually this involved developing pieces and relocating them to places where they have an active role.
Feel free to ask me anything by messaging me if you like because the middlegame isn't easy at all, but I hope this points you into the correct direction
I'm not at all familiar with whatever terminology there is, so please forgive me on that part.
What am I supposed to do after the early game, or "book move," phase of the game? I've been only playing against the beginner bots for a bit and I've only either ended up failing or resigning because... after the early game, the plans that I have just fall apart. It's like every move past the third or fourth turns are blunders or inaccuracies. It's been incredibly demoralizing and unfun to see.
I'm not keen on getting a membership for lessons so I ask: what medias should I look for to improve past the early game?