Would these shifters work on a 90s MTB with cantilever brakes as a low-cost recycled gravel bike? How can you ID the number of speeds of the shifters?

Yes, they will work with cantilevers.
Those are most likely 3 x7 shifters. Hopefully the ratchets still function; they are rare to find in working order, given their age.

You can just count the clicks as you shift. Ideally with a cable in them and a bit of tension on the cable (so it doesn’t jam up). 7 speed will have 6 clicks.

As others already stated: these are old! expect them to work only after some lovin.
probably 2×7 (source: i have them on am ’90s roadbike)
like for anything vintage parts, finde the stamped numbers and check out velobase.com
(in your case the sticker on the front plate should do the trick. btw the front plate is in the wrong direction, the cable should route to the bikes center, the writing shouldnt be on its head)
short pull brake levers will work with cantis, but be sure to fit them to their derailleurs to not run into compatibility issues

I did this for a home made gravel bike. You’ll find the lever doesn’t have the range for cantilever brakes, BUT if the wheels are very true, and you can align them really well,there will be enough range for the brakes to be effective. For number of gears, click and count, provided they still work