tldr;
To solve this problem I had to install the linux-kernel 5.15, still in RC (rc3). linux-5.15.rc3 fixed the problem : now bluetooth works
thank you gog and zbe
/tldr;
Well,
I’m answering myself, as the problem is solved thanks to nice people, gog and zbe on chat.
The lsusb command gives the id of bluetooth controller. It is : ID 0489:e0cd Foxconn / Hon Hai Wireless_Device
zbe sent me this page https:/ /marc.info/?l=linux-bluetooth&m=162575050725913&w=2
about a recent implementation of bluetooth driver in linux kernel. Look at line :