Can't seem to find anything related to rules around trades, beyond signing extensions in either of the rules or CBA docs I've skimmed...
But, I found a sportsnet clip featuring Friedman and Brian Burke (94s long) dating back to Feb 26, 2020 stating that a player acquired post TDL is eligible for regular season games, just not the playoffs. Link below.
However, this could have been changed in the last CBA making us both right.
Edit: to include link and date of clip
EDIT2: I mean a player agent should know whether a post TDL transaction allows for players to play regular season games... But a former NHL GM definitely would know.
The only logical reason for both to be stating the opposite is for a change in the rules between Feb 26 2020 and March 22, 2022.