I tried the solution on my Brother MFC-J6920DW and MFC-J6940DW. The latter was specially purchased new because the 20DW turned out to be incompatible with Windows 11. Unfortunately, the solution does not work on both machines. I had silent hopes because after a week I had been working with Brother's IT specialists here in the Netherlands, without results.
Unfortunately, we have to wait and see what solution the IT guys from Brother and Microsoft will come up with.
Interesting, as the MFC-J6940DW is MOPRIA certified for the Print/Scan features where the 6920DW is not. One would think that going for this Mopria certification as a basis for compatibility would have satisfied your connectivity. Clearly the issue is outside just drivers - as they state:
" Windows also supports Mopria certified devices making printing and scanning easy whether you are at work, at home, or on-the-go. When installing a new printer or scanner, and a Windows Update is not available, Windows will automatically install the Mopria certified printer or scanner."
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