No, Homey Pro (Early 2023) will support Matter and Thread probably somwhere in the future, See RoadMap Homey Pro - the world’s most advanced smart home hub.
The Bridge probably doesn’t need matter as Homey will support it, Thread is not an option for the Bridge.
See: https://support.homey.app/hc/en-us/articles/7263667137052-Setting-up-Satellite-Mode
but that is also under development.
The bridge is pretty simple so only supports the RF/IR and maybe other protocols up to what is specified.
No.