I'm not sure this was established canonly, but I thought Breen ships could cloak according to some throwaway dialogue on DS9 and TNG? Do I have that wrong?

Is the ship too OP to be fitted with a cloaking device either inherent with the ship (easiest to do for both Fed and KDF) or maybe a cloaking device console?

Nope. The dialogue was speculation, and even then, only some Breen ships would have been able to cloak.

In-game, the point is moot, as no Breen ship in-game can cloak, not even NPCs.

It's also possible that they used soemthing more like mask energy signature....

I think it's this.

Unless they captured a ship that did cloak and reverse engineered the system.

It can cloak now with the T5 Romulan Rep ability... too bad it only lasts 3 seconds :p

No wonder the Dominion lost. Things might have turned out differently if the Breen had useful training for their science officers.

I think that in Typhoon Pact they get cloak from Romes

The Typhon Pact doesn't exist in the STO universe, so no-go there. Furthermore, if the Breen got cloaking tech from the Romulans in Typhon Pact, it probably means they didn't have it before that, therefore they still don't have it in this universe.

But yeah, I wouldn't put it past the Breen to use energy dampening on themselves as an MES of sorts.

It never was at any point.
Not even DS9-era soft-canon material include this.
The explanation in the "Tales of the Dominion War" novel for the successful attack on the Sol System mentions the Breen using a holocloak (which we already have ingame) combined with firing their energy dampener at ESD to disable it.

Yes you do.