Like you said, when a minority coach or executive leaves the team that developed him to accept a Head Coach or GM job with another team then the original team gets two 3rd round comp picks. So yes, the Rams do get a 3rd round comp pick in both 2021 and 2022 as a result of Brad Holmes leaving the Rams to take the GM job in Detroit.
However, those comp picks are separate from the comp picks teams get for their FA losses. IOW the Rams could get 4 FA comp picks in 2022 in addition to that 3rd round comp pick for Holmes (for a total of 5 comp picks!!).
From this article: [
profootballtalk.nbcsports.com]
These compensatory picks are in addition to the 32 compensatory picks that are regularly awarded. So while the draft would typically have 256 overall picks (32 in each of seven rounds, plus 32 compensatory picks), there can now be more than 256 picks because of the additional compensatory picks.
AlbaNY_Ram