So after logging in to https://i.mi.com/?_locale=en, I only had my redmi note 7, so I deleted it, and did as you said, I went to Setting>Accounts & Sync. But the only options I found there was Auto-sync data, which was off so I turned it on, and Sync now, which I did. But even after that, my Poco X3 Pro still doesn't show up in https://i.mi.com/?_locale=en
Not quite sure how to deal with this issue though. It can be server side issues.
Turn off Find my device and then turn it on again with internet connected, may also try turn on GPS accurate location.
If this makes device show up, then should be fine.
If this does not work, maybe turn off Find my device function and try unlock this way.
I'm not very sure if the Xiaomi account need to have a mobile number tied to it in their website for that account to be able to unlock bootloader. In the past maybe it's not required, but policies may change.
If still not work, maybe log out both Xiaomi account on PC and phone, try create a new Xiaomi account with mobile phone number, then use that new account to login on both PC and phone.
You might need to request unlock bootloader again, so another 7 days to wait.