How can I publish a blog and newsletter with complete anonymity?

The blog part: create an .onion or .i2p site. Or create a site elsewhere but always do any related tasks through Tor at the very least (including account creation and email usage).
Not so sure about the mailing list part.

If you have that threat level, I hope you are already protecting yourself against spying on your web searches. With no protections, you could easily become a target by just looking any of these things up.

Riseup’s Purpose

The Riseup Collective is an autonomous body based in Seattle with collective members world wide. Our purpose is to aid in the creation of a free society, a world with freedom from want and freedom of expression, a world without oppression or hierarchy, where power is shared equally. We do this by providing communication and computer resources to allies engaged in struggles against capitalism and other forms of oppression.

☞ https://riseup.net/en/security

or/and https://www.autistici.org

We believe that this world is far from being the best world possible. We react by providing a platform and tools for digital self-defense addressing the need of free communication for activists and other individuals.

Which services do A/I provide?
We provide a suite of communication tools:
Email
Blogs
Mailing lists and Newsletters
Web Hosting
Instant Messaging and Chat
Videoconference and Streaming
Anonymity Services

Mastodon via tor.

If you live in such a suppressed area. Tor might be your best bet. Hosting the site on a .onion address.

I think you can publish on many ordinary (micro)blogging platforms through Tor, but you'll need a valid email address.

So the problem is reduced to: how can you get a valid email address through Tor that is not linked to either a phone number, your real identity, your credit card, or another email address that has any of these pieces of information stored.

I have never needed to do this, but to my knowledge, there are email providers where that is possible. Another user linked to privacytools.io where I can find this list https://www.privacytools.io/privacy-email - so that may be a place to start.

I find rentry.co/ really useful if you are planning on posting a few blogs, Like for example you can make these pages through tor or a vpn

rentry.co/Liam

rentry.co/Liam-CIA-Blocks-God

rentry.co/Liam-I-Vaporized-Elon

Just make text backups of the pages in case they are taken down

I don't think the tools on privacytools.io fit your requirements (maybe globaleaks) but this site is a good start

https://www.privacytools.io/blogs https://www.privacytools.io/private-hosting https://www.privacytools.io/secure-whistleblower

Also some of the privacy messengers here (like Briar) have blogging/forum features similar to Telegram, but you can't access them via a browser, so you would have to get everyone to install those apps:

https://www.privacytools.io/privacy-messaging

But realistically speaking like the others suggested: Tor, I2P, Zeronet, etc..