It works! You saved me.
Indeed, althouth all OpenXR was disabled in my project, turned out that my OpenXR layers were still active by the time I was using my old Vive with SteamVR.
For anyone facing this issue, I suggest to use OpenXR-API-Layers-GUI since it is very easy to use and does the job (disable all the layers should me enough)
Many thanks @Rectus_SA