Does the gmail SMTP server have a limit on how many emails can be sent per day?
I think it does, yes. The kinsta.com link says the limit is 500 per day. If you're expecting a higher volume than that, or if the unpredictability of relying on a free Google service for anything is not acceptable, then you would probably want to pay for an inbox service.
But if you're running a small instance and just need the occasional email to go through without a lot of effort or fees, then it ought to be fine.
You got yourself a new sub. Thank you for sharing!