I've learned a couple of things as I'm slowly transitioning my email from Comcast to Gmail:
Email newsletters sometimes have a link at the bottom to change your subscription to use a different email address. Sometimes they just have an unsubscribe link.
When changing an email address with a provider, even one who has a "change subscription" link in their newsletter, it doesn't always stop emails to the old address. Sometimes I've had to change the subscription to use the new address, then unsubscribe the old address when I get the next email twice.
Some websites use an email address as your login ID, so those are easy to find and change using the list I printed from my password manager. However, most websites still use your email address as part of your profile or contact information, even if it's not your login ID. I've found that I have to change pretty much every account, even if I don't use the email as the login ID, because somewhere in that profile they've got my old email.