I did the instructions on Proton's website to enable the browser flag but I don't get a "Google Password Manager" prompt at all. The only passkey prompt I get is for USB, NFC, and "this device". Proton Pass doesn't show as one of the options, nor does the Google one as described in their screenshot with the Proton name written under the logo.
I'm using a Pixel 6A with Play Services installed. Using Vanadium. The OS and apps are up to date as of date of this post. Proton Pass says passkeys are supported in their app menu on the phone. I was able to set up a passkey in Proton Pass for Cloudflare on PC, but not on my phone. I tried Outlook.com. Same result. I only get the hardware passkey options.