WiFi Calling on Pixel 5 appears to be semi-blocked by NextDNS.
I say "semi-blocked" as it will sometimes appear as active (e.g. Vodafone UK WiFi Calling scrolls across the top of my screen) when NextDNS is enabled, then it will dissappear after a minute/5 minutes. Toggling on/off doesn't help. Disabling NextDNS does help.
Checked logs for my phone, cannot see anything obvious being blocked.
Your device is probably checking the quality of the connection and finding it's not quite good enough to work as well as your cellular connection.
A Wi-Fi connection that is not explicitly set up to work well for VOIP will often not cope well with simultaneous use of the same connection to the Internet for VOIP and other things that transfer lots of data.
Here in Germany, the same problem exists with Telekom. The cause is that foreign DNS servers are not accepted by Telekom for Wifi Calling.
Here is some information from a technical forum (but in German):