There's an argument that this should be done with domain names as well. Right now, anyone can buy an expired domain, set up a wildcard email address, and read any email that's still being sent to addresses in that domain.
Conversely, if you take the advice of some to set up a personal domain for your email, you are basically committing to a lifetime obligation. If you later change your mind and let that domain expire, any future owners of that domain will receive any email that was sent to your old addresses.
Domains are like real estate. You may end up with a nuce prime real estate in cheap & do nothing. You bought a good domain long ago and not using it. You may buy a domain/property, raize everything & start from scratch. If you abandon a plot/property, domain, and not pay the dues (taxes) or registration fees, anybody can come & claim it through defined procedures.
Same way I may buy a home & get mail. Tomorrow if I sell that home I need to do change my address with senders, and make sure to put forwarding (maybe keep the old domain for few weeks/ this year)
No standard way to inform the sender of a new address, AFAIK.
You can set up a forward to your new email, and keep the old address active and forwarding messages until you're satisfied you've updated (or canceled) all the uses of your old address.
Then maybe start bouncing messages for a period of time before you finally shut down your domain.
https://9to5google.com/2023/05/16/google-account-delete/