what are the thinnest (physically) Yamaha PSR keyboards ?
I want to buy one strictly for midi controller use because of shallow key depth and good key feel.
need it to be thin, unlike the majority of them, so it can fit under my desk.

Sorry man. Most of the newer ones don't even have real MIDI jacks. The Arturia Keylab Essential has a pretty small footprint. Or a used CMK-149, maybe the smallest ever (at least with fullsize keys)! My $.02.

As long as it has USB.
I had arturia 25 key before. Currently I have NI control a61 and s61

WARNING...check out the MIDI capabilities first, they don't necessarily make good MIDI controllers. Look at the detail data list to see exactly what MIDI messages are sent from which ever kbd you are looking at. Check to see what if any MIDI msgs are sent from various switches, knobs etc that you want to use.

If all you want to do is send MIDI note messages, pitch and mod wheels control msgs......no problem.

All I need is: keys, pitch / mod, octave and transpose. All PSR-S / Tyros transmit that.
Just need to find one with mod and pitch wheel that’s pretty thin, and not to pricey.

Anyone know what keybed is used in Tyros and PSR-S keyboards ?

PSR-S keyboards use the lower end light touch keybed that most people can get along with but some hate it. It's the same as is fitted to the lower end PSRs. For info, the new SX model keybed is a longer travel and heavier weight version of this keybed.

Tyros / Genos use the FSX Keyned which is top notch in my opinion.

None of these keyboards are notably thin. I'd vote for a controller. Whilst never had a play with the Arturia models they talk a good talk!

I tried Genos at guitarCenter once, I much prefer the older keybed of PSR-S series and older Tyros (tyros 1 ).

my playing comes out much better on those keybeds,
probably because 25+ years ago when I started playing keyboards (cheap $200 yamaha psr) thats the keybed it had and thats what I'm used to.
Weighted (piano) Keybeds are a total nightmare for me.

btw, I played, (or atleast tried playing) accordion few times, and also like the shallow key-depth of accordions

If you need both pitch and mod wheels, you'll have to step all the way up to a PSR-s710 (or s750, etc.) There are some tiny PSRs like the PSR-E323 that you could buy for $100 on eBay. But no pitch/mod.

Some of the mid-line models like EW-410 and PSR-s670 Edit: PSR-s650 have only one modulation wheel.

All of these PSRs are bigger and thicker than they would need to be for your purposes because they have speakers and at least some arranger controls.

There are tons of controllers on the market, I guarantee one of them has the keybed and controls you want in a smaller footprint. My $.02.

Vadim - shows how individual we all are.

I first played a Tyrps 1 and Tyros 2 at a local launch show for the Tyros 2. And it was no contest, the T2 keybed suited me perfectly whereas the T1 felt way too light! I've come from acoustic piano which probably explains a lot.