Oh definitely don't get a pi 400. They're just a pi 4 but in a keyboard.
https://www.amazon.com/Raspberry-Pi-7-Touchscreen-Display/dp/B0153R2A9I or
https://www.amazon.com/Elecrow-Capacitive-interface-Supports-Raspberry/dp/B07FDYXPT7/
There might be smaller ones out there.
It was actually fairly simple (direct Amazon links):
ELECROW Raspberry Pi Touchscreen Monitor 5 inch HDMI Screen Display 800x480
Cable Matters 2-Pack Ultra Thin HDMI Cable 3 ft
90 Degree Right Angle Micro USB Male to 5 Pin Motherboard
I cut the top two tabs off the HDMI screen with side cutters and it was a perfect height to wedge into the basement window without any connectors. In hindsight I did not need the 90 degree right angle on the micro USB, but it still worked. I am using AIDA64 with one of the 800x480 sensor panels I found on this forum thread. I have tweaked it to use the values for my machine and that was it.
There is a picture in my post history, but I'll take another with the flash on https://imgur.com/a/amRqDCW. The black screws and standoffs I am using came from this kit: https://smile.amazon.com/gp/product/B07D7828LC/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1 They work well and I used the longest spacers to get the screen as close to the glass as possible. The hdmi I have is a 270 degree elbow cable and I have a 90 degree micro usb to 5 pin like I mentioned. https://smile.amazon.com/gp/product/B072Q1MBSG/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1 This helps keep the cables tidy. I see you did yours to the top, I routed my hdmi under the gpu and out the pack next to the pcie bracket.
I have this variant of the same screen. Yes, when the PC hibernates, goes to sleep mode, or powers off the screen reads "no signal" for just a moment then powers off. I am not sure if that's a function of the screen itself or the motherboard or some other reason. I have the aorus b550i and it's powered through a usb mobo header to micro usb plug. https://smile.amazon.com/dp/B07FDYXPT7/ref=dp_iou_view_product?ie=UTF8&psc=1
Wow, I had read that cooler wouldn't be compatible with the glass panel. I'll keep that in mind if the need to change my cooler every arises.