Security

When I am on Flight Aware, this pops in at the top of the pages:

FlightAware has detected a problem with your email account. Please click here for more information.

I cannot imagine how Flight Aware could even see my email account. I believe this is a fishing probe.

Well the link you provided leads to a page on the flightaware webpage.
(Fishing would typically have a link that leads to some dubious website)

That page just states that FlightAware is unable to deliver Email to you for whatever reasons.
They can easily detect that when they send you the newsletter and the mail to the address you provided comes gets “returned to sender”.

So Flightaware is not saying that your email account isn’t working, it is just saying that they can’t deliver mail to it.
(Which means you either misspelled your address or their mail is being rejected. That on the other hand you could say is a problem with the address you provided.)