Guitar strings suddenyl start touching fretboard? - eviltoast

Hey guys, i’ve got a weird thing that I might have fucked up a bit, but any tips are welcome.

I’ve got an old cheap guitar which I though I’d improve a bit with some other pickups I had. Installed the pickups, also got some new strings. So weirdly enough, for some reason the new strings touched the first few frets. I could adjust this at the bridge but it really needed to be lifted a lot, which screws up the action in my opinion. Didn’t screw with any other part of the guitar besides pickup, the only reason I could imagine was that the neck was warped from sitting around without strings for a bit (but it wasn’t even that long I believe? But maybe cheap guitar = cheap materials?).

The neck doesn’t seem warped to the eye, but have to admit that I’m starting to doubt the straightness of my references for straightness. It feels as if the neck is ever so slightly crooked on the body (like leaning forward a bit), but again I can’t imagine this suddenly happening when changing the pickups?

I know some might say “just take it to the shop” but I like DIYing and I really want to learn more about this stuff, and especially what the hell is going on. Anyone got any thoughts on this?

(Could post some pictures but on pictures nothing really stands out).