To be honest, the brakes drag slightly, even without the handbrake connected with the natural effect of the supposedly adjusted brake pistons against the pads.
Yes, the brakes do drag a bit with handbrake off, so make the adjustments so you feel the brakes
drag a bit more when handbrake is on 1 click. When you release the handbrake, check the additional drag has vanished and there is play in the cable at the rubber concertina boot at the caliper and to confirm it is not pulling pulling on the caliper.
For my car with factory fitted calipers and original pads:
Before adjustment (car was 9 years old in 2018): 9 clicks maximum (stretched cable?). Car rolled on slight gradient with 3-4 clicks. Held with 5-6 clicks. Too much travel in handbrake lever imho. Still passed MoT though.
After cable adjustment: 7 clicks maximum. Car holds stationary with 3-4 clicks, like when car was New.
I'm no expert but I would have thought only new cables may be required if the original is seized and/or not moving freely, or has stretched so much to prevent any adjustments to compensate.
Other thought is as you just fitted new pads, perhaps they just need a bit of mileage to bed into the old discs too.