how rare is B+B vs. B+B endgame?

IDK

If it's same colored bishop endgame, or maybe opposite colored endgame, then it's fairly common. If you mean both sides with two bishops, that's pretty rare.

Not rare at all. In fact, I had the following game in the second round of an over the board weekend event last weekend.

Hello

fairly rare but nothing crazy. naturally certain openings lend themselves to such a position more than others. I actually got this imbalance in my last tournament.

actually this may not have been exactly the moment both knights were traded, i think the 2nd pair was traded later, but this is still an example of a position where both knights being traded is not uncommon so the double bishop endgame arises.