The only signings we have that counts toward the "free agents gained" category is Sanders and Burton. Jenkins doesn't count since he was released and Peat doesn't count as he was re-signed by us.
The Sanders deal ($8M APY) may cancel out Klein's loss ($6M APY) but I haven't checked out the OTC cancellation chart. Burton's deal isn't large so I wouldn't doubt if it even reaches the cutoff threshold.
EDIT: Yup, he's projecting the Sanders signing cancelling out the projected 6th rounder we possibly could've received for losing Klein. https://overthecap.com/compensatory-draft-picks-cancellation-chart/However on the plus side, the 3rd round compensatory pick we should get for losing Bridgewater possibly might be the 3rd-earliest compensatory pick awarded (would be pick #99) since only Brady and Rivers signed deals for a higher APY ($25M APY) than Bridgewater ($21M APY). So barring any other QB's getting paid big money (or maybe a pass rusher that's still out there), we should get the 3rd highest compensatory pick.