That stroke:

On your side, both hands forward, top-side hand a bit further forward with shoulders tilted towards that arm. Top hand comes back (using forearm-to-hand as a 'flipper'). Stroke back has a bit of down-angle to it, face pointed to top shoulder so body coming up a bit plus forward motion makes a 'pocket' of air. Inhale. Continuous slow exhale through the rest of the stroke. Top hand (now in air) comes forward, inserted in water as it was through a door letter slot. At the same time, bottom hand goes back. Pause a bit (the 'catch').

Part of the 'drive' comes from shoulder-tilt - which also let me be a bit longer in the water (Froude's Law). Ditto feet folded back (true for every stroke). Legs are doing scissor-kick, double the rate of arm-stroke or the same as, depending on how far I'm going. Scissor lets me catch and glide there too and so get more distance for each bit of effort.

The nice thing about the stroke is that, in rough water, I can just put my back to the spray (inhaling spray and the consequent bronchial spasms are... bad. Not just uncomfortable but put me back in the pack).

I've shown people (mostly kids) how to do this. If I saw a kid who was a 'sinker', I'd introduce myself to the parent(s), let them assure themselves I wasn't some kind of pedo, then teach, with a focus on gliding and making the body long in the water, emphasizing the glide with "swimming's for lazy people!". I'd had a fairly miserable time learning to swim on the surface when I was a kid; if I can spare somebody else, I’m in.

I've never written the stroke out like this - and probably missed something important.

For anyone else: if you know a 'new paradigm' crawl, it's this, turned into a sidestroke so I can inhale, but with scissors replacing flutter. It’s a very un-dramatic stroke; nearly no splashing. If you’re splashing, slow down, pay attention to being both graceful and long.