They may have been disbanded by the French King and his papal lackey, but they didn’t cease to exist. Many sources have them going to Scotland, Spain, Germany, Portugal the New World, etc. The Knights of Christ and Teutonic Knights were offshoots of the Templars and the Hospitaliers inherited some of their fortune. The Knights of Malta still exist and some say Freemasonry is descended from the Templars.
The Knights Templars mostly joined the Knights Hospitaller, another military order
Those in Portugal renamed themselves the Order of Christ, in Spain, Order of Montesa -- as the Reconquista was still going on
There were no Knights Templars in Scotland post their dissolution -- in fact the Templars were tried in Scotland in 1309 -- 3 years before the French King unjustly and falsely implicated them. The Knights in Scotland were absorbed into the Knights Hospitallers as you correctly said
But the Templars as a distinct organization ceased to exist
They did NOT get absorbed into the freemasons who started off as a trade guild and later degenerated in Europe to an anti-Christian organization (in the US it returned to being a social club).