As a test, I imported a cuesheet with 22 tracks into a FLAC file using metaflac (--import-cuesheet-into="cuesheetname.cue" "flacname.flac").
However, I noted that each different TITLE on the original cuesheet has been changed to Track 01, Track 02, ... Track 22.

I examined the result with foobar2000 I noted that the single FLAC file now appears as 22 independent files, each one named Track 01, Track 02, ... Track 22 (which suits my needs!).
Also, I have been able to edit the content of each track and change each individual tag: Title, Conductor, Band, etc.

Since metaflac changes titles while importing, is there a tool that's able to import a cuesheet into an existing FLAC file but preserving the original information?

You can use two options to preserve your original cuesheet verbatim:
metaflac.exe --import-cuesheet-from="image.cue" --set-tag-from-file="CUESHEET=image.cue" "image.flac"

The "--import-cuesheet-from" option is intended to store just the minimum necessary information for CD burning (no CD-TEXT etc.).

Tested and verified that it works as intended.
Thanks a lot for the clue (I note that the second option may also be seen with the --help option, but I missed that!).