Backend quota exceeded (I know it's been covered, but...)

OK, I found some numbers, but they look odd. Total’s nearly a thousand GB. Is it a combined value?
On Ubuntu 22.04, df (and everything) gives me only 0s for /run/user/1000/gvfs. I don’t have mtp.

Expected behavior of a setup like this is unknown to me. The available here looks about 500 GB high, meaning we can’t trust it even if we could get it, if it’s actually true that 334GB is the available amount.

  --quota-size (Size): A reported maximum storage
    This value can be used to set a known upper limit on the amount of space a
    backend has. If the backend reports the size itself, this value is
    ignored

The last sentence IMO has too much trust in the backend and subsequent reporting code, especially if destination is Local folder or drive simulated by who-knows-what-mechanism. There’s an old issue for

and if this were allowed, perhaps it would provide a general way out of a predicament like the current.

Backup Quota Warning Error #4970 has some comment but is waiting for information from originator.

Backend quota has been exceeded after apparently successful backup has earlier technical analysis.

There might be other short-term solutions, e.g. rather than use media transfer protocol, use a network.
There appear to be FTP (somewhat insecure unless encrypted) and SSH servers you can investigate.