I did a lot of research on this and the most important thing to think about is the layout. Is this just going to be to input a little bit of text every once and a while, or will you type a bit on it? The reason is almost all folding keyboards have to make layout compromise in order to fold. Some squish certain buttons down, some add gaps, some remove buttons entirely.

I wanted as close to natural button placement as possible, with USB-C charging, at a decent price. It didn't need to be the most premium thing because I just use it every once and a while. I went with this:

https://a.aliexpress.com/_mP3WQ8u

It doesn't however have a touchpad like you want. I made a spreadsheet where I collected all the main folding keyboard and you can sort by accurate button layout, touchpad,, multi device support, price, etc. Note that I made this a while ago for my own purposes so the prices will be old and some links may be dead. Hope it helps.

https://docs.google.com/spreadsheets/d/1deduytlpeEHGsTo-mvWg4MxDUsHnf_iCSsAJCa51h6g/edit?usp=drivesdk

I've got this one and it's been a godsend for setting up things in Desktop mode with Steam closed

Samsers Foldable Bluetooth Keyboard with Touchpad Portable Wireless Keyboard with Stand Holder, Rechargeable Full Size Ultra Slim Pocket Folding Keyboard for Android Windows iOS Tablet & Laptop-Gray https://a.co/d/91zi2fT

I bought one off Amazon and it was garbage. The hinges popped after 2 or 3 openings.

I recommend these keyboards as they are small and seem to get the job done well enough.

My work bought an expensive one for me when they had a little money left in the budget last (fiscal) year. It was about $80 and seems to be fairly tough. Not sure if it's worth it unless you have the cash lying around, lots of non-folding keyboards are the same length/width as the steamdeck.

The Steam Deck track pads are going to be better as a mouse than anything on a keyboard.