Hi merryheart777,
welcome to the Apple (user-to-user) Community.
Re: "Pages -- separate open windows become tabs when opening a new file"
Seems the + sign icons in Pages can be confusing.
ie the + at the top far right opens a new tab in the current document (not a new window, or page, as one might expect.)

while the + for add page on the left just adds new pages to the current document
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Re: "The separate windows collapsed into one window with two tabs. Is there a way to disable this feature? "
For Mac OS 12.6 (if you have upgraded to Ventura, things may be different!)
Seems that may have been accidentally triggered somehow. (Maybe by swiping ?) I could be wrong. (There is a menu command for "move tab to new window")
As far as I can tell there are no settings for either opening in new Windows or in Tabs,
as the tabs are only added with the + on the top right.
Was unable to replicate what you experienced when I tried opening page after page on my Mac. (both with, and without, using the chooser for new pages)
Am often working constantly with three or more open docs, each in its own window, leaving and returning. The only way tabs appear is when I click the + icon.
From "Windows" in the menu bar, using the drop-down menu, tabs can be moved to a new window however:

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Re: And to have documents default to opening in windows, not tabs?
Seems that is already the default. (Works as such on my MacBook Pro 15")
(Am assuming however, that you are still using Monterey MacOS 12.6 like me)
So I guess I'm not much help to you here:
If you are having multiple appearances of tabs and windows "misbehaving".
You might want to send feedback to Apple about Pages behaviour.
They will likely not reply, yet if others are also experiencing similar occurrences,
(eg: maybe on certain Mac models) there may be changes in a future update.
Online Webform : Feedback - Pages - Apple
All the best :-)