There are two separate issues in this topic, related but not intrinsically tied together.
The first is whether the file format supports any kind of marker in the metadata.
The MP3 file format is very ancient and does not support markers (nor gapless playback and other features that modern codec/container combinations do support).
I believe that the mpeg4 audio files which are usually labeled as .mp4, .m4a, or .aac files support markers. For use with free/libre software solutions the Ogg container format which is typically used with Vorbis or Opus audio data supports chapter markers.
Chapter extention for VorbisComment tags
The second issue is how to get track markers within Ardour exported as metadata markers in your format of choice.
That is not something I have personally done, but according to this page of the manual it looks like if you export with the checkmark for chapter markers for MP4 files created, it should do what you want:
Ardour manual export format profile page
I do not have access to a machine with Ardour at this minute, so I cannot check whether that forces you to use Apple Music export profile, or if you can use other codecs. I would expect that it would be specific to MP4 files based on the name of the option, although also based on the name it seems that it makes a file with chapter marks, so it is not clear how you make use of that file.
What type of file you use may depend on how many different types of playback devices or software you wish to use. You mentioned VLC, which supports nearly every file format, so should no be a problem no matter which codec and container you choose.
If the export dialog does not have options for creating the appropriate metadata, my first inclination would be to generate a WAV file and CUE file from the CD export setting, then make a script to convert the CUE file track entries into chapter entries in a comment file for an ogg or opus file, and call oggenc or opusenc as appropriate to encode.
That is basically what Ardour does behind the scenes (although probably using ffmpeg), so a lot of the pieces probably already exist to do what you want.
I would start by looking through the options for generating mp4 files, there may be a combination which already does what you want.