Only happens with a Drop Frame Sequence start time set to any timecode.
After Exporting, Sequence Start Time goes back 1 frame from lets say 00:59:45;00 to 00:59:44;29.
Using Info Tab, original file on V1 shows timecode of 00:59:45;00. Sequence time is 1 frame before that after performing an Export or cueing in ME.
Export again and the Media Start TC in the new file is the 1 frame earlier

Also, some video exports are ok with TC from sequence matching the Media Start time. WAV exports show Media Start of 0 and do not match the sequence TC.

Just export any audio/video or audio only file, bring in the exported file and check the Media Start time TC in the Project Bin.

Update regarding timecode not being embedded:
In the Export Tab, make sure "Metadata" is turned on.
Inside there, you can select "Minimum Required". This is new to ver 2021 and 2022. In 2020, I had it turned off as I wasn't exporting Captions. Issue resolved.

Bob K.