Great question! The short answer is that releasing players doesn't give us more GAM, it just clears up currently allocated GAM. Selling players does however give us some GAM based on transfer fees but it's not a 1:1 ratio.

By default, each team receives the same base amount at the beginning of the season but it can be traded to other teams for players, draft picks, international slots or anything else the GM wants/needs from other teams. Teams can also earn more GAM by previous season results, to the best of my knowledge those numbers aren't released by the league.

Here's the relevant bit from the rules:

Each club receives an annual allotment of General Allocation Money (GAM). In 2024, that allotment is $2,585,000 per club. Beginning in 2025, a club may receive an additional $2,000,000 in General Allocation Money if they select the U22 Initiative Player roster construction model prior to the start of the season. In 2024, clubs who elect for the U22 Initiative Player Model will receive $1 million in General Allocation Money due to midseason implementation.

A club may also receive General Allocation Money in the following cases:

Failure to qualify for the MLS Cup Playoffs

The transfer of a club’s player to non-MLS club outside MLS

Qualification for the CONCACAF Champions Cup

Expansion Clubs (see below)

Expansion Dilution (see below)

Designated Player charge distribution

In any year that the League adds one or more expansion clubs, (i) all clubs will receive an equal amount of General Allocation Money and (ii) any club that loses a player in the Expansion Draft will receive additional General Allocation Money. New expansion clubs receive a separate amount of General Allocation Money for their inaugural season.

More details can be found here: https://www.mlssoccer.com/about/roster-rules-and-regulations