> Instead, send them a politely worded one-time announcement with an invitation to subscribe.
NO. DO NOT DO THAT !
That is terrible advice and it is against the law.
Opt-in has to be done without inducement and of a person's own volition.
Sending a mail to someone saying "pretty please sign up" is not valid opt-in. It is spamming a bunch of people hoping they will opt-in. It does not matter if you got their mail another way (e.g. if they purchased a product, you can't then spam them trying to get them to opt-in for your mailing list).
One of the fundamental reasons the opt-in law exists is to stop people doing the shit you suggest and ensure that lists are correctly built in a clean manner.
Under GDPR, can someone send an email to people who 1) downloaded our app, 2) voluntarily entered their email, viewing a message that says if they do that, we can send them a newsletter about how to be more efficient with the app, and 3) selected what kind of person they are, e.g. a teacher, marketer, etc.
But it's been 10 years. Can we send them a newsletter now with an unsubscribe link? Does GDPR have an expiration date on that stuff? Yes it was affirmatively opt-in.