They won’t, only incoming UFA’s count towards the compensatory formula.
And you nailed the rest of the post.
Additionally another thing Belichick does is they’ll trade peanuts (6th/7th round picks) for decent players with a year or two left on their deals, pump up their value in their system and then they’ll either let them walk in free agency and let another team pay them a big deal or they’ll trade them again if they can either:
a.) get a 3rd or higher pick, since a 3rd is higher than a compensatory 3rd, or...
b.) at least get a higher pick than they gave up in the initial trade and higher than they would get as a comp pick by letting the player walk (and they get it a year early instead of having to wait)
Lots of suckers in the league that routinely fall into that trap of paying their fringe talent players that they don’t want.