Everything seems to have some sort of meaning, but the peacemaker just feels random.
Why does Marty give the colt peacemaker to Seamus at the end of Back to the Future Part 3?
Part of the running joke WRT Seamus's hat, IIRC.– BCdotWEBOct 11, 2021 at 9:09
In my opinion it is kind of memorabilia which Marty is leaving behind for Seamus.
We can also interpret it as a symbol of courage which Marty stood up for and defeated Tannen.
Since generation of McFly has always been bullied by that of Tannen's, it was a symbolic message from Marty to Seamus for being courageous so that coming generation of McFly can stand up for themselves.
Also because Seamus didn't have a gun and Marty didn't need it back in 1985.