Mounting to an old pan-style electric box

Can you replace the pancake fixture box with a steel one? Is it fastened to the ceiling joist with long wood screws? Turn the power off before doing this.

Probe through the screw holes. Is there any obstruction within an inch directly above the box? There is one knockout left unused in that box. Can you push or pull it out? Doing so will give you room to get one finger on the top side of that box...

Retrieve the nuts from on top of the box or acquire new nuts. Insert thin wire (a conductor or pair from CAT5 cable, floral/craft wire, thermostat/bell/irrigation control wire, etc) up through a screw hole and pull the end back down through the knockout. You'll have a roughly U-shape wire path from screw-hole to knockout. Slide a nut onto the knockout-end of the wire and use the wire to guide the nut so that it sits on top of the screw hole. Insert a finger through the knockout and use it to hold the nut in place while removing the wire and starting the screw into the nut from below. Repeat for all four holes.

Next you've got to tighten the screws. This is most easily done with an impact driver. Use short intense bursts of motion: with each burst the screw will turn a little bit relative to the nut, tightening the connection just a little bit, before the nut accelerates to match the speed of the screw. Some back pressure against the nut can be a big help. Use a prying tool to put tension on the screw-nut assembly, pulling the nut against the top side of the box. This increases the friction between the nut and the box and allows each drive burst on the screw to accomplish more. You might even be able to find an amount of tension where manual tightening of the screw works.

Finally, install a knockout seal to cover the hole.

The insulation on your wire appears in good shape, I would suggest an old work ceiling box. You can leave the old box up there if you want but most likely will need to trim some of the plaster for a new box to fit. Most of the new “old work” boxes will be plastic and will support a standard light fixture but not a chandelier or ceiling fan. This is what I use when the old box is damaged, as a best practice I will normally slide some heat shrink over the cloth for a little extra protection incase the rubber is brittle.

How annoying! OK get a set of drills and start sticking drill bits up through those holes -- butt end first. We just need to know the hole size.

Now hit a "Drill and tap" table. Anytime you tap a thread into a hole, you drill the hole to the smaller size (tips of the threads). Go to the table under "Fine thread bolts" and find the fine-thread size whose drill size is slightly bigger than the holes you have. Buy the correct drill and tap, drill, and tap.

Now you have what you thought you had in the first place.

You need to use fine-thread because coarse-thread won't have enough purchase.