Wow, thanks Jo22, doshea and bakemono for your responses! I'm genuinely impressed there's other people out there who care about this 😀
It seems Borland made an effort to refresh the dialog boxes with large colorful buttons (nice!), but the Xtree functionality is really what I was looking for. I'm unable to remember if Xtree was the exact program I was using at the time, but these basic file operations were definitely part of it. I'm pretty sure I got mine from a shareware CD that came with a magazine. I still have many (maybe all) of them, so if I happen to run into it, I'll post here if it was indeed Xtree or an alternative.
In the meantime I remembered that WordPerfect 6 also had a nice extended file dialog. It also had "bookmarks" in the form of a modifiable "quicklist". Of course this dialog was only available within WordPerfect, but still. Posting some screenshots below for anyone interested.
WordPerfect 6.0 file dialog:
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Compare to standard windows file dialog:
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Quicklist "bookmarks":
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File options:
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