"cannot verify server identity"- but no associated email account on device

Settings/General, scroll to the bottom. Look just below VPN for either Profiles or Device Management. If you find either open it and look for a profile that has a familiar name. If neither exists we need to check other options. The most likely is an app or a calendar.

Go to Settings/Passwords & Accounts, and look under Subscribed Calendars, and if you find one delete it. That’s my best guess for now. After that go to Settings/General/iPhone Storage and carefully scroll through the apps looking for one that is related. It’s easier to find apps here than by searching through the Home screens.

What makes you believe this is a mail issue? Your message states it says that it cannot verify a server, and you say it shows a URL. Did you use this website to send messages out? Was this website saved to your device as a bookmark, or something similar?

You may also wish to check Settings>General>Profiles and see if there is a profile that was installed to use with the website. A mail server issue would have identified the account and/or an email address info. It seems you only use iCloud for mail on the iPad. Is that working alright? Curious more than anything. You can also go to Settings>Safari>Clear History and Website data in case there was a cookie from that website.

Interesting. If you go to that website, is there any support link there that may address the issue? I wouldn't know a reason it would randomly display that for a website. If you go to Settings>Passwords & Accounts, is there an account listed there you do not recognize?

Alright, that message that you are seeing deals with the website's certificate being expired. That would help explain the error you saw, but I still can't figure out why it is appearing if you are not trying to go to the website. I'm going to see if someone else I know can look at this.

Pretty much any TLS (authenticated, encrypted) network connection will check certificates.

Not limited to mail.

And far more than web browsers use HTTPS (HTTP over TLS) connections into web servers.

And other not-HTTPS TLS network connections, too.

Look for a web browser client refreshing its top sites previews, or any RSS reader or such that might be used with that website.

Check in your saved iCloud passwords, too. (That shouldn't cause this, but it’s also harmless cleanup.)

Confirm there are no mail accounts. Yes, I know you stated that, but this being troubleshooting, confirm it.

Check the settings of any apps you were using to access or manage with that website.