So first off, not sure if you're in a different country or something, but I live in the US, and basically every website, Government or not, has a way to easily change your email address.

I've run into one or two that I had to call to confirm, but still, it was pretty painless.

Second, gmail allows you to automatically forward your emails to a different email address. While you're going through the process of changing your primary email on different websites, set up a universal forwarding rule on gmail to send all emails to your new address.

Third, for actually transitioning your emails, sit down and write a list out of all your services that are tied to your email starting with most critical first. This would be banking, auto bill payments for utilities, car payments, credit cards, phone/internet payments, investment logins, etc.

Basically, the sites that if you lost access to or couldn't auto pay with, you would be screwed or at risk of late payments.

Getting all of those down should be pretty quick because there shouldn't be that many unless you have a ton of different loans, banks, and investment portfollios.

Getting those taken care of will take your stress down significantly. Then move on to important, but not critical, this could be your streaming services, other subscriptions like news sites or newsletters, important apps or services you pay for.

Then tier three is everything else. Stuff that doesn't really matter that much.

This is what I did and now I'm completely off Gmail/Outlook and onto Protonmail and love it.

Last thing to remember is to download anything in your email that might be important. Just force the rule to run through your whole inbox and it will forward all your old emails to your new address. This will likely take many hours to fully sync, but eventually all email records will be moved over to your new email address.