kinda annoying that Microsoft made the "mail" app move to "outlook (new)", because now it will get confused with the full version of "outlook", so instructions like "file menu > account settings" for keeping no limit offline or rebuilding cache are useless advice to outlook NEW people (like an AI answer that gives you hope, but is more like regurgitated misinformation)
I feel you: it's very frustrating to not have control over what "sync" deems important (one folder seems empty, because it only has some old emails, yet another one might have an older email in it; but, we the people know we put important emails in that folder, so we could easily access later, so are they lost?! kinda scary)
note: in "outlook (new)", in settings (the cog icon), in general, see "offline":
you can pick "180 days" in that drop down menu for "days of email to save" (but lacks a "no limit" or "all", like outlook has; and note, you'll need to make whatever folder a favorite: right click on it, and add to favorites), so that's at least something
TWO CHOICES (in my opinion):
sticking with MS: use edge and webmail just for the archive/old stuff (and certainly continue to use the convenience of Outlook NEW, aka "outlook (new)", for the daily inbox checking, and trust sorting emailing into folders--just don't think you'll always be able to access all emails with it)
or fugedaboudit MS (and having to use two methods to access email): go to the Microsoft Store, search for "Mozilla Thunderbird Email"; small learning curve, but troubles over (no thanks to MS, who's like a three trillion dollar company--the people will pick up your slack for free)