does this look right?

Your siding is to close to the roof. If it had a gap of at least 1", replacing the step flashings would be a simple process.
The flashings may be okay, can't tell from the pictures.

There should be a step flash for each shingle. No way to tell from the picture. We always put in new step flashing except on rare occasion.*



*We might reuse existing step flashes if putting new in meant too much damage to siding, the old step flashes were in good shape and the pitch of the roof was like a 10/12 or more so water went downhill in a hurry.

Ah, so there could be flashing underneath all this?
I'm completely new to this so just trying to understand how it works.
What would you recommend doing now to improve the gnarly-look factor?

Give it a few heavy storms to make sure it's not leaking.
If it's not leaking, scrape and paint to make it look better.
If it is, you'll need to have the siding cut back to allow replacement of the step flashings.

you could gentle lift a corner of each shingle near the siding and feel for the metal flashing piece. Each step flash should end just under the shingle enough so you can't actually see it exposed.

Does the contract for the new roof include words like "replace step flashing"?

Look at #9's pictures, all those right-angle pieces of aluminum are called step flashing, it goes under the siding, bends and ends up under the shingles. When a roof is replaced, the roofers usually pull off the old ones and slip new ones up under the siding, and then put the shingles over it. It's hard to see if they did that here because the siding is tight to the roof, which it should not be.

They might not have pulled off the old flashing as #3 said, because there were maybe too many nails through it in the siding. It's too bad the roofers didn't suggest they cut back the siding for you before they did the roof.

The siding can be cut back now, but the danger is that someone might cut through the siding and into the aluminum flashing, defeating its purpose. You could also have the bottom courses of siding removed, cut new pieces that clear the roof by an inch or two, and put them on.