Over 1000-year timeframes, the biggest changes in technology and warfare come from the unlikeliest of sources.
1000 years ago, Eurasian warfare was dominated by steel edges (axes, swords) and human-propelled projectiles (spears, arrows). Only in a corner of modern China was the Southern Wu military adding a pouch of black powder to arrows to create an explosive incendiary warhead in the form of "fire arrows". Who knew then that obscure invention would be the first step on a path of innovation leading all the way to modern sidearms, assault rifles, machine guns, mortars, rockets, howitzers, missiles, and bombs.
1000 years ago in the BT universe (circa 2150), warfare was still dominated by tanks. The key technology enabling battlemechs, myomer, was still 200 years away, and the first battlemech farther away still.
It's these discontinuous innovations that dictate the nature of warfare a millennium in the future. Projecting better swords and arrows from 1000 to 2000 would have totally missed the advent of firearms, rockets, and canons. Projecting better tanks from 2150 to 3150 would have totally missed the advent of the battlemech and its cousins.
It's really hard to say what discontinuous innovation currently present in the BT universe would come to dictate the nature of warfare circa 4150. But if I had to offer an option, based on limited and crude Blakie experiments with weaponized HPGs and K-F drives, I would assume some form of practical weapon that utilizes K-F fields by 4150 (or well before).
Honestly, given that the first functional K-F drive emerged in 2107 and the first functional HPG emerged in 2629, it's surprising that practical K-F weapons have not appeared in-universe. That's like inventing and using nuclear power plants and liquid propellant launch vehicles for hundreds of years, but never creating a nuclear weapon or ICBM. Regardless of where it's invented, technology is almost always and rapidly made dual-use (civil and military).
FWIW...