Is the Caro-Kann Defense: Advance Variation winnable for black?

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It's fine.

Don't worry about openings; just focus on not blundering

@1

"Is the Caro-Kann Defense: Advance Variation winnable for black?"
++ No, chess is a draw with best play for both sides, and Caro-Kann is sound,
and the Advance Variation is no better or worse than other variations.
 
"I noticed that I struggle when playing the Caro-Kann Defense: Advance Variation."
++ What do you mean by 'struggle'?
 
"I haven't studied the opening" ++ No need to.

"that's probably the main problem" ++ No, but you need to analyse your lost games.

"it doesn't look like any of the players had much success when faced with the Caro-Kann Defense: Advance Variation playing as black." ++ Black is OK.
 
"it looks like black ends up losing the majority of the time in this position."
++ That is a misinterpretation. The results correlate with the player ratings, not with the opening. When stronger players as black prefer Open Games, or Sicilian, or French over the Caro-Kann, then results of the Caro-Kann go down. When stronger players as white prefer the Advance Variation over other variations, then the results of the Advance Variation go up.
 
"Should I just try to avoid getting to that position by playing a different line that wont lead to the Advance Variation?" ++ No.
 
"i cant get my queen side knight to f6" ++ So your king's knight should go elsewhere e.g. Ne7.
Likewise you cannot get your queen's knight to c6 in the Caro-Kann, so it should go elsewhere, e.g. Nd7, or you should spend a tempo for ...c5 and ...Nc6.

"everything just feels super closed" ++ That is no problem.

Here is an example game:

What I like about the Caro-Kann is that I need to know only little theory.

Thats a huge advantage if you're older and cant remember openings that well anymore.

Just replay games of GMs of the same opening. After s dozen games, you will play the opening by intuition.

Get your bishop out, exchange it off, and play for pressure on White's center with the knights and a timely c5 break.

Something like this? (This isn't mainline or anything, just an example).

Study Alireza Firouzja’s Caro-Kann games, with very aggressive and successful results.

U2000 games are decided by blinders. Most popular opening is playable including Caro Kann advanced. Review Master's games under B12.

There are a million videos and dozens of books on the Caro-Kann. And many thousands of master games. It is winnable for black if white doesn't play perfectly, and even the top GMs today make mistakes.