I too am dubious about it being the brakes. Tyre pressures affect grip and some tyres are more sensitive to pressure than others.
Also, if your rear wheel has had a lateral knock that's shifted it slightly out of line, that can affect grip when any other variables are.... well, varying. Meaning if you're braking, turning, accelarating or similar, a wonky wheel will exacerbate any tendency to lose grip.
You may think you'd know instantly if your rear wheel was not quite aligned. Not so. It's worth checking.
As a last one, if your bearings are gone your rear can move around a little and that can also affect grip where grip is already limited. I suspect you'd know if your bearings were mashed, but it's worth a thought.
Finally... do you have some sort of oil or lubricant on your rear tyre? If it's not on the contact patch you may not be aware of it, but if it's on the sidewall of the tyre it may make you lose grip when cornering and you may think the cause is the braking, not the lean angle.
Good luck finding the cause anyway... nothing is quite as unnerving as a bicycle given to erratic behaviour for reasons that aren't clear.