A lot of people notice the POP problem when inbound mail stops. Others notice it when they reply: the customer sees an @gmail.com sender instead of info@yourdomain.com. Those are different wires.
Check mail handled inbound. Send mail as uses the other provider’s SMTP, or Google’s infrastructure if the domain lives on Workspace.
Sending checklist
- Confirm the host allows authenticated SMTP.
- In Gmail, open Settings → Accounts → Send mail as.
- Verify the address with the code you receive.
- Send a test to an external account and check SPF/DKIM in the headers.
If you solve fetching with GetPopMail, you still need outbound mail set up on your side. Sync does not invent magical SMTP.
Recommended order: get inbound working first, then fix the From address. Mixing both problems on the same day is how you lose track of what broke.