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OP there is no quick way to do this, nor should there be, because it would mean there is a service which is aware of all your subscriptions at the same time which makes it that much easier to dox you.
You'll have to do it one by one. I find it's best to simply make a list of all the subscriptions you can think of off the top of your head, since those will be the most important ones, then change all those over immediately. After you do that, just occasionally drop in your old email to see if you're still getting stuff, and switch over any subs you still care about.
I would suggest keeping your old email account as a back up or burner account. I personally maintain 4 email accounts simultaneously for active use and have over a dozen if you include burners I frequently use.
