You can use any OTP App or device of your choosing. TOTP is a simple standard for 2FA which is why nobody necessarily needs Google or Microsoft Authenticator.
There is Aegis, FreeOTP, OTPManager (iOS/macOS) and many others. Some Password Managers like 1Password, BitWarden and KeepassXC also support OTP.
Switched to Posteo about a decade ago
That could be since I don't know Tutanota. But an email provider who doesn't support IMAP/SMTP sounds kinda weird to me. But mailbox.org doesn't need their client. They support normal protocols: https://kb.mailbox.org/de/privat/e-mail/e-mail-konfiguration/
- only web app
- needs client app
What's up with that misleading information as if there's something missing? This just means you can use any mail application you want with the standard mail protocols IMAP and POP3. If a mail provider is offering an app themselves that's fine but that's nothing a mail provider HAS to offer. What's much more important is how they handle you data, how good they filter out spam, how big you mailbox can be, cost, sustainability etc. But the app is the least important thing.
That's just satire. That "quote" is so obviously not a quote.