Probably bottom bracket issue
 

Exceptional experience today: 18 miles into a ride, suddenly the cranks seized completely and I couldn't pedal. I had noticed some creaking noises, but thought they were coming from the handlebars, particularly when I stood up on the saddle. The "solution" was very low tech: I flipped the bike over and pushed as hard as I could, which worked - for a while.

Twice more in a stretch of 18 miles this happened, and every time it happened, I was pedalling with the non-drive side.

There are three visual items I wonder about:
1) the cup on the non-drive side sometimes rotates, though only a few degrees. Should it be completely tight, and can this be a problem?
2) there appears to be a shredded piece of black elastic between the crank on the non-drive side and the cup.
3) Both cranks have a very small lateral wobble when pulled and pushed back and forth manually.

Thanks in advance for tips, hints and clues, which I suspect may include "dude, get a new bottom bracket"

Is this a cartridge or cup & cone BB?
Pics might be useful.

Sadly, I don't know, but here is a picture.
https://cimg7.ibsrv.net/gimg/bikefor...e9097efcfc.jpg

I think that's one of the newer styles that I'm ignorant about.
Maybe a PF-30?
Hopefully someone can help.
Maybe this will help?
https://www.bicyclepartsdirect.com/bb30-vs-pf30/

Jesus...you're not much for cleaning/maintenance, are you? SRAM? You for sure need a new bottom bracket, and I'm guessing your crank axle is most likely very corroded. Maybe more photos just so we can provide accurate advice.

I'm not much into detailing bikes, but I'm pretty sure I'd have spotted the aluminium of the BB beginning to corrode or it becoming hard to ride the bike.
New BB is needed. I can't tell the difference between a SRAM and Shimano BB fitting on looks (I don't care that much), but it's a cheap swap with that sort of bottom bracket.
Since you didn't know what was wrong, maybe take it into a bike shop and have them do the swap. It's quick and easy.

I also agree that maybe you should take a look at the crank axle too. From the looks of the corrosion, it may well be in really, really bad form. And if I read the "pedalling with one foot" as in the two crank arms not connected, it is definitely finished, and you need a new crankset.

Edited to Add: No, you don't want the "cups" to rotate. At all. Of course that's a problem. At this stage, I'd count myself lucky if the BB tube isn't worn out and useless, setting you up for an expensive fix.