Gmail doesn’t lie and it’s not weird at all. They support standard IMAP client setup and it is true IMAP which “stores the mail on the server” and “syncs the same mail to all the clients” just like any other mail server does with IMAP setup.
Gmail is only different in the way it setups up mail folders where “they are folder (labels)” connected to All Mail “which houses all the email” and you can also apply “multiple labels to a single email”.
So when you add a Gmail account “you must enable All Mail in your Gmail account online” to then be able to sync all the folder (labels). All Mail is enabled by default in your Gmail online.
eM Client support wrote a good blog on Gmail All Mail and how it all works and why you need it.
If you don’t like Gmail Folder (labels) or the All Mail folder housing all the mail, then contact Google as that’s the way they designed it years ago and it works perfectly for most people including myself.