BIAB puts the chord (spelling in as a Marker field)
Reaper can read the markers and put them in the marker field.

Studio One has to process imported MIDI notes or Audio to recognized chord spelling and put them in the Chord track. It can then drive MIDI and/or Audio track tuning via the chord track.

IFAIK Cubase also can recognize chord spelling from MIDI data or Audio data to load into its chord track for use with MIDI tracks.

IFAIK Cakewalk and Logic currently do not have chord tracks.

Music XML can spell 33 types per chord for chord charts.
So, I would say the best options for now is:
Options 1: Output a MIDI file:
- MIDI block chords for systems that recognize the chords +
- Chord names as a marker in the MIDI file for systems that recognize the markers and put them in a marker track
Option 2: Output a Music XML file:
- Music XML if you're workflow involves notation.

Studio One (latest version), Win 11 23H2 , i9 -10940X 3.3 GHz, 32GB Mem, a 4K 40" monitor, PreSonus Studio Live III Console as interface/controller. secondarily test on Reaper, Cakewalk, and S1 on Surface Pro 3 Win 10 (latest versions).