I believe we do this to retrieve the invoice but from there need to make a call to a app on mobile to actually make the payment. So basically from a browser (PWA) to local mobile wallet app like WoS.
Not sure this is possible right now..
Discussion
You'll have to go through the mobile OS wallet selector using a custom url scheme I believe. This requires a user interaction though. Or Nostr Wallet Connect could be an alternative solution.
Thank you! This helps a bit. I will look into how to call the mobile OS wallets from a PWA. Nostr wallet connect is interesting though, will consider it as well.