I'm a bit biased here, but towards the end, the Republic was probably the most unique doctrine, tactics, and units of any faction. Though thanks to how they died, we only see it in XTROs and a brief section in Blood Will Tell (BWT). HotW failed completely to show it, and I'll try to avoid dumping on that novel with what should have happened.
It's from a mix of hardware and the strategic situation:
- Drones that canonically are seeing revisions as counters are developed.
- Superheavies
- ClanSpec production in house
- RISC
- Shared tech between RotS and FedSuns
- combined arms doctrine because of an originally fundamentally defensive army setup
How's that applied:
1) Drones allow for a couple things thanks to the celerity, revenant, lament, and lich (and presumably others not shown given the number of RotS mechs without sheets).
1a) Canonically, celerities are used for blinding fast response, and the operators are known for being aggressive. In BWT there is the spike celerity that's engaging in 400kph ramming attacks that crippled multiple MAC units that can't really track or counter them.
1b) Conjecture: There's no reason the other drones couldn't be used similarly. RAF had an excess of hardware, but less people. Drones enabled a way for RAF to go hard against targets in what otherwise would have been suicide attacks. So now you've got units ranging from blinding fast lights, to simple support lights, to cav heavies, up to a direct fire assault that can be sent on one way missions with much less
2) Superheavies create a wall or a hammer and act as a force multiplier. It's not just the psychological impact of the giant mech dwarfing even an atlas. It's also the dedicated Tactical Officer (not a mechanic beating the piss out of a barely functional mech to keep it running as HotW depicts it) coordinating the ares and surrounding units.
3) RISC - despite IO, RISC somehow reached a stable-ish quality in Shattered Fortress and seems to be equipped to Stone's Brigade, the Fides, and even some Hastati in enough numbers that enemy commanders are seeing and being forced to address the new tech.
So now you have an army comfortable deploying in combined arms down to even the smallest deployment, with ground elements that can respond faster than anything short of aerospace, with elements that don't sleep and can sustain harassment at all hours (by swapping drone operators), with elements quite okay with going on one way attacks to cripple a target or your supply train that would be secure against any other army, and with strange mechs rocking new hardware in combinations not seen before that make them - per Shattered fortress - have an edge in duels and mech on mech battles that puts enemy commanders on edge. And they've spent the last several years raiding to hone a combat edge.
Or... you have HotW, where the RAF is presented as a mostly mech army with vehicles that don't do anything, and has superheavies but no superheavy doctrine.