https://simplelogin.io/ (owned by Proton) is great for this. They have a feature to generate an email address by random word or even by uuid.

Are these emails you need to memorize? Diceware would work.

Otherwise I'd just use something like simplelogin and just have it automatically generate one. Then just save it in your password manager.

There is anonymity and pseudonymity.

Do you need your opsec to be resistant to state-level actors (oppressive regime, censorship, illegal activities)? Well then you need to make sure you don't introduce anything that will deanonomize you.

Are you trying to be resistant to mass data collection efforts used for profit? Being on the pseudonymity spectrum is a good step.

Dealing with the latter is like dealing with a bully. Make it not worth their time. They just want to put you in bucket X so they can estimate the most likely way to influence you for reason Y. Pseudonymity is about having multiple aliases that get put into different buckets so their privacy invasive efforts are less effective.

For me I use ddg email aliases with bitwarden. It's great and free. I tried others but ddg works great but doesn't have any of the bells and whistles.

Use an anonymous email proxy like (https://)addy.io . Create an email address for every site.

Hopefully, I haven't misunderstood your question.

That is a good idea just so that you don't have to think about any potential privacy issues. Your email could be {firstword}{secondword}{4 numbers} and so long as the words and numbers are randomly generated, you can avoid accidentally including personal references or biases.

Your username does not need to be high-entropy, though. It will be semi-public. So it's not about strength against dictionary attack or similar, it is just about leaving the selection process up to a random process that isn't witnessed by a third party. You can write scripts that will generate these kinds of things using Python and the faker library.