You can check out Crinacle's definition of BA timbre here, which I quite agree with:
https://crinacle.com/2019/02/04/what-is-technical-ability-according-to-me-myself-and-i/
His description of "Plastic timbre" AKA BA timbre = some weightless and hollowness in notes due to a too fast decay. Usually this is more apparent in treble frequencies for acoustic instruments such as woodwinds and brasses for example.
However, not all BA types suffer from bad timbre, for example the Sony M9 uses some foam to damp the nozzles so the timbre is quite natural.
And timbre is very subjective. Some are not particular about it, and value other aspects like technical chops over timbre. Some listen to music genres which do not emphasize acoustic instruments but more of synthetic ones (so timbre may take a back seat). Some have not heard a real acoustic instrument up close so they don't have a baseline for timbre to compare with.
So nothing right or wrong, we have different priorities, and maybe it might be a blessing for you not to be picky about this so-called BA timbre!
This is the original BL05, not the S variant which is green and is the one
@Jmop bought.
The original BL05 sounds like a metallic tin can. Super sibilant and harsh in the upper mids, with a metallic timbre as described above by Crinacle.
The sequel BL05S is legit but avoid the original BL05 IMHO.