Yes wifi6 is backward compatible with other wifi versions.
The problem you have is all extenders like this use a feature called WDS to do this. WDS was not actually intended to be used for this purpose but most manufactures now implement it the same way even though there really is no official standard. Most routers have WDS so they should work with repeaters.
The "mesh" systems use another method and you can not mix different brands of mesh systems in most cases. But even mesh systems will support WDS to be compatible with older repeaters.
I would consider every other option before you buy any kind of repeater. This is where you will be happy to get any kind of signal rather than no signal. It also is not just plug...