[0] https://lichess.org/training/themes [1] https://lichess.org/training/fork
Because of that I doubt doing problems of the former kind will help seeing forks much when going back to “find the best move” type problems.
Before you can do that, you need to understand the moves you can make and their implications. I think identifying forks fit here.
I’ve been enjoying the Dr Wolf app, which mixes lessons, actual play against a very forgiving CPU opponent, and spaced repetition of mistakes.
I tried Chessable but the UI was awful and beginner/learning content was poor.
Disclaimer: I'm the creator of BraiMax Chess. Any feedback is welcome.
These are quick tactical puzzles, that adjust the difficulty to your level. Put in some hours, and you will spot obvious forks!