Good question. I recently bought Jovanka Houska's "Opening Repertoire: The Caro-Kann" and decided to explore that.
I recently played 4 daily games starting from this position as black. I really liked how the games progressed. For right now, that's my response to the advanced variation.
Both Stockfish and Lc0 appear to put 3. ... c5 about equal with Bf5. I say appear because I haven't let them run for terribly long at this position. I recommend Jovanka's book. So far, I like it.
Why is Botvinnik-Carls defense in the caro kann ( 1.e4 c6 2.d4 d5 3.e5 c5) uncommon at the masters level. I mean I couldn't find many master games in the database.