After installing SSMS 22 (22.0.0+103.11205.157) and updating SQL Complete (v2025.3.61), all SQL Complete settings seemed to have copied over successfully and work as intended. 

The only feature that seems to not work is SQL Complete tab coloring. It was previously working on SSMS 20, but not on SSMS 22. I deleted all tab color settings and repopulated to no avail. The status bar does change to match the SQL Complete tab color settings, however, the tab colors itself remains at SSMS 22 default.

See screenshot for example. Note that SQLQuery4 is connected to the configured tab color setting, the status bar reflects the setting but the SQLQuery4 tab does not.