1. Buy a domain. About $10/year for a .com
2. Buy a /24 ipv4 block with good reputation (maybe like $10k)
3. Get a rack in a nearby datacenter, rack up a BGP-capable router and your servers for redundancy to run email. Takes about $30k initial setup costs if you buy all new, and about $5k initial setup costs if you cut corners and buy used. It'll be $2k/mo after that, so less than the cost of 1 $100 avocado toast per day, quite affordable.
4. Setup your mailserver of choice, such as dovecot + postfix. Enable either a catch-all address, or use recipient_delimiters. The former means "anything@domain.com" works, and the latter means "user-anything@domain.com" works (assuming your recipiient_delimiters are '-'). I recommend using a real catchall.
5. Setup your spam setup, this is the hardest part. I have no guidance here.
6. Point your DNS over, setup SPF and DKIM records, test, and off you go! This should all take about 1 to 3 days if you know what you're doing.
7. Find out that some email will go to spam anyway because you're not using one of the big 4 email providers, but it can't be helped, and anyway no one uses email anymore.
And after that, for less than $30k/year, you have email with catchall or subadressing support. Nice and easy.
You can also pay Fastmail for email and use their "catchall" feature https://www.fastmail.help/hc/en-us/articles/1500000277942-Ca...
Or Google Apps also has a catchall feature.
Then, after you do this, you can simply give internet archive the email address "internet-archive@mydomain.com", or generate a random string. If you forget the email you used, you can search your email history for the first email they sent you, and check the To field.