I've had some setup to get notified by email in the past. I've been using blockchain.com and the interesting part is that I've added an address there (i.e. watch only). There were clearly privacy issues, but no safety concerns since blockchain.com didn't know private key or seed. It was years ago and I don't know if it still works like that.
It may be off topic, but I'll add another possibility: if push notification on your smartphone are also OK instead of e-mail, blue wallet does the job, and again, you can just add an address (watch only, safe) there. Of course, same privacy concern applies.