I don't think that's possible but I'm not 100% sure. I know in Daily chess games, you can save notes. You can save your game with annotations like the one you showed but it would take a long time to do for every single game you played.
Question about analysis, adding notes and saving games
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Is it possible to save a game with notes/variations like this in chess.com? The UI can be confusing sometimes and it seems like a must have for a chess website.
https://lichess.org/study/9XAhbaE7
On the forum I see someone comment like this
I would like to save games with notes/variations like this for myself to look at and revisit in the future. Hoping this is possible and someone can guide me to the right direction. Appreciate any help.