Discs: non-starter.
From the contemporary
'mag' review:
"the real let down here are the Tektro R540 Dual Pivot calliper brakes. They just don’t work very well. At the very least the brakes are consistent; just consistently poor."
I agree with
@si_c : get some Koolstop Salmons for at least the front. This assumes that your brakes have shoes (ie the pads slide into them and are secured by a tiny screw). Even if you get new brakes, you'll need decent pads and they are a top choice.
The rest of the groupset is Tiagra so you could find some of those (105 and Ultegra are the next two steps up, in the Shimano hierarchy).
https://www.wiggle.co.uk/shimano-tiagra-br4700-front-brake-caliper/
Note that if colour's important to you, check it.
One Roadbikereview reviewer offered this advice:
"These brakes came OEM on my bike and at first they were completely squishy and the toe in came completely miss adjusted. Toe in is adjustable. There is a hemispherical surface on the P422 adjustable angle cartridge pads that allows angle adjustment by how it meets the washer. To adjust toe in, place 0.5 mm shim at back of pad with screw loose and tap lever several times to align pad then hold lever tight while tightening screw. Once the pad angle is properly adjusted these brakes are not squishy at all and stop silently. This toe in adjustment is apparently a huge problem because many reviews mention problems caused by angle errors and some even solve these problems by installing non-adjustable pads."
Might be worth trying this first; then decent pads second.