I have no subvol=/ option at all:

Probably depends on kernel, but I presume missing subvol means the same 
as subvol=/ .

I am only interested in mounted volumes.

If your initial path (/local/.backup/home) is a subvolume but it's not 
itself present in /proc/mounts then it's probably mounted as a part some 
higher-level subvolume, but this higher-level subvolume does not have to 
be root. Do you need volume root or just some higher-level subvolume 
that's mounted?

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With Best Regards,
Marat Khalili