Reaper doesn't have a dedicated chord track hence ReaTrak, it uses Regions, (hopefully Reaper 6 will have a chord track) but actually Reaper will do it better as it can get the chords from, a midi item, BB Chord Output midi track, Biab RB PT musicxml export, midi markers, midi lyrics, cues and it will also get the plugin chords.
I'm just looking into scripting in Cubase and Studio One to get the plugin chords from the plugin's Song.txt in the bb folder.
(Chord=bar,beat,name)

Chord=1,1,Am
Chord=2,1,Dm
Chord=3,1,Em
Chord=4,1,Am
Chord=4,3,G
Chord=5,1,F
Chord=6,1,Em

there's also the part markers that Reaper gets
(PartMarker=bar,A=1 B=2)

PartMarker=1,1
PartMarker=9,2
PartMarker=17,1
PartMarker=25,2
PartMarker=33,1

To get them into bandLab you need chord midi markers, that I have been asking for in BB RB since 1834 smile
You can open the musicxml from Biab RB PT in Reaper get the chords then save the track as MIDI with markers, then open that midi in BandLab.

Biab Track Injector for Reaper
Free Biab Chord Picker Tool