An apparently related issue is being investigated in the context of MicrosoftEdge/WebView2Feedback#951.
A known workaround is to set an environment variable like so:
COREWEBVIEW2_FORCED_HOSTING_MODE=COREWEBVIEW2_HOSTING_MODE_WINDOW_TO_VISUAL
The downside is that this completely defeats normal Tab key handling inside the page.
Somewhat related: https://codingguides.quinnscomputing.com/2022/05/how-to-allow-moving-focus-to-and-from.html presents an idea how to have a WebView2 control take part in the superordinate tab sequence.