Windshield tape pulled paint off when I removed it - who pays for this?

That tape pulling paint off means the paint was already lifting. Properly bonded auto paint will not come off with masking tape, even after a couple days in the heat. The tape test is literally how shops check paint adhesion, and it takes scoring the surface with a blade plus much more aggressive tape to make good paint let go. So the tech prolly didn't do anything wrong, and neither did you leaving it on an extra day. The paint just let go at the weakest spot when given a reason.

White is the worst offender for this too. The pigment in white paint can accelerate UV breakdown of the layers underneath over the years, wich is why you see so many older white cars with roof and hood panels peeling. The fact that your roof already looked faded next to the rest of the car fits that pattern. It was a failure waiting to happen. That said, I'd still call the glass company and file a report. It costs you nothing, and sometimes they'll send someone out to look at it. Just don't be shocked if they come back and say the same thing, that the paint was compromised before the tape went on. Keep the tape if you still have it, and take some clear photos before the bare spot gets dirty or starts to chip further.

On the fix, a touch-up pen is the wrong tool for a patch that size. Pens are for stone chips the size of a pencil eraser. Anything hand-sized comes out lumpy and shiny against the surrounding paint. For a spot like that a body shop would sand the failed area, feather it out, repaint the roof and blend into the pillars if needed. On a white solid color with a faded roof, they'll likely want to do the whole roof anyway so it doesn't look patchy against the sun-beaten original paint.

If you want a cheap stopgap, clean the bare spot well and hit it with clear coat just so it doesn't rust or keep peeling further until you decide what to do.

Similar thing happened to my old white pickup a few years back, except mine started peeling on the hood with no tape involved at all. I just left it and within a year the flaky spot had spread way bigger, so the clear coat stopgap idea makes sense to me. Wish I'd known to do that back then. My worry now is if this is a paint that likes to let go, will the rest of the roof start flaking off on its own even after a shop fixes the one spot? Or do they sand past whatever the bad layer is when they redo it?

Same story here with a glass swap on my wife's sedan, except the tape came off clean and the paint still bubbled along the trim line a month later. What saved the roof from spreading was a roll of quality painter's tape I pressed over the edges of the bare spot while I waited on the body shop quote, kept the flaking from creeping. Shop ended up blending the whole roof anyway, said patching a faded panel always shows. If the glass company does offer anything, take a cash settlement and pick your own shop.

Update: took the first reply's point about the paint already being loose and called the glass company with it. To thier credit they didn't fight me, sent a guy from a local body shop to look, and the roof got sanded, repainted and blended last week. Looks fine now. He confirmed the spot was flaking before the tape ever touched it, so at least the tape was just bad timing.