Singer 7466 lost timing
I fixed it after studying it a bit longer. Here's how:

First, I noticed that the dog feed makes these four basic motions over and over:


Up
Back (away from you)
Down
Forward (toward you)


Second, my wife clued me in to the fact that the dog feed should not move the fabric while the needle is down.

Now, these two things are probably very obvious to everyone on this site, but not to someone like me with very little exposure to sewing!

I loosened the relevant parts so I could freely spin the bottom shaft independent of the top shaft. Then armed with the above two pieces of information, I put the needle at top dead center and the dog feed at the threshold between its motions #1 and #2. Then I tightened things down so that the top and bottom shafts were locked together again. I spun the hand wheel to confirm the needle was never down during the entire duration of the dog feed's motion #2. That put the needle in time with the dog feed.

Next I needed to put the spinning bobbin holder thingy (what is that called?) in time with the needle. I did that by loosening the grub screws that tie its rotation to the bottom shaft, then I rotated the hand wheel and turned the bobbin holder thing until the eye of the needle was just below the pointy hook bit of the spinning bobbin holder thing on its way up. Then I tightened those grub screws. That put the bobbin holder in time with the needle.

A quick test with power applied confirmed the machine was happy enough with my timing. I reassembled everything, got my wife to teach me how to thread things up, then impressed her with a working straight stitch! It sews a straight stitch forward and backward just fine.

The machine also needed the dog feed to be realigned a little bit because it was impacting the plate, but that's not really relevant to what we're talking about here.

Unfortunately I didn't see any timing marks anywhere. Had there been timing marks I would have tried to make sense of and use them. Also, while the gouge marks in my picture would have made it possible to tell exactly where the pulley had been before it slipped (thanks for that idea, @fixer1234!), that knowledge would not have helped because I had already taken off the timing belt between the top and bottom shafts--doh!

Disclaimer: neither my wife nor I have any idea if the machine is correctly doing any of the fancy stitches, because neither of us really know how what they're supposed to look like lol! All I can say is the machine didn't lock up or catch on fire when I tried a zig zag pattern. All it did was pull the fabric together which might be normal, or maybe the tension was wrong?