The performing “forces” would be another name for the armed “forces” who are mostly dancing but occasionally singing.
Generally, the characters who sing, Washington, Hamilton, Lafayette, Hercules, etc are singing to represent the course of events that took place over a MUCH longer period of time. The Battle of Yorktown was around 20 days. There may have been times when time stops are slows down, the dancers do stop at one point and then seem to move in slow motion,
so your answer there may be “both.”
The music prominently features “The World Turned Upside Down” which was an actual song sung by the American troops after defeating the British, but it also draws upon melodies established earlier in the musical such as “My Shot.” The rest of it features a good deal of beats which seem to represent a “bell” ringing (every few moments you hear some type of clang or clash) which may not only represent the “liberty bell,” but also sometimes represents “doom.”
The music is jovial, in some cases almost like a hoedown during the dancing (Yorktown is after all in the South), but also representing liberty and in some cases death.
The dancing is done by the soldiers to show how the expert military formations devised by Washington, Lafayette and Hamilton outmaneuvered the Brits’ tactical methods.