> I wonder if the same can be done with Gmail archives.That's called "using an email client" to access email.
The way it originally worked, you know, and still does[1].
I use Vivaldi browser, which has a built-in mail client[2]. You can use Mozilla Thunderbird[3], or (gasp) Outlook.
All of them allow you to maintain a complete, offline, up-to-date copy of your mailbox, which you can export and back up if needs be.
[1] https://en.wikipedia.org/wiki/Internet_Message_Access_Protoc...
[2] https://vivaldi.com/features/mail/
[3] https://www.thunderbird.net/en-US/