I personally avoid Blake3 and stick with blake2.
I personally avoid Blake3 and stick with blake2.
Yes, the core of blake3 is a modified blake2b with fewer rounds, and yes the person who wrote the "Too much Crypto" paper is one of the blake authors, but there are other aspects of the construction that contribute as well.
Blake3 operates in a merkle tree mode using the modified blake2 as a node hashing function, which, in and of itself complicates attacks for reasons explained in the blake3 paper. Blake2 also didn't really have that many rounds to start with, Blake3 only reduces the round count from 10 to 7. A good _most_ of the speedup in Blake3 is due to the change in construction, the merkle tree mode allowing for unbounded parallelism, and not having the SIMD-friendly version be a variant. The parallel variants of Blake2 are already _almost_ as fast as Blake3 even without the round reduction (hell, BLAKE2sp can actually be faster than Blake3 in the right conditions).
Though, note, blake3 still provides enhanced resistance against the attacks against blake2 even in the case where you only have one block, due to the change in how the fundamental hashing primitive is used.
Given that the best attack against ChaCha fails to break ChaCha8, it's reasonable to conclude that BLAKE3 is secure.
A fully optimized implementation of BLAKE2bp/sp is about 2x faster than BLAKE2b and more than 3x faster than BLAKE2s. That's an enormous speedup. Consider that SHA-3 has a reputation for being slow, but the software speed difference between SHA-512 and SHA3-256 is smaller than this. There are some complications when you get into short input performance, but any application that needs to hash files (where short input performance is dominated by the cost of opening the file) would almost certainly be better served by BLAKE2bp/sp than by BLAKE2b/s. In that sense, I think the biggest practical advantage of BLAKE3 is just that it doesn't ask users to navigate these tradeoffs. We discussed this a bit in the intro section of the BLAKE3 paper.