Tablet case, with keyboard in the exterior of the lid

for the iPad 7, 8 and 9th gen there is the Logitech rugged combo .
Keyboard is permanently attached

for the iPad 5th /6th gen the Logitech rugged combo, has its own version of the smart connector with lightning connector for power
Keyboard is detachable

most newer iPads have keyboard cases from Logitech that use the Smart connector.

There are some videos on it and amazon has it for $100 at this time. It looks like keyboard is inside and the top closes and lock the iPad.

The one from logitec does not need to be recharge. It uses the iPad for battery. No cable to the iPad. I got the apple smart keyboard is nice but does not have a build in case. Now that I saw the one mention, I might endup getting it when amazon has their June deal.

Sorry to say it, but I think you’re going to really struggle with this. In addition to the narrow market for such a device that you mention, any case I’ve ever come across locks the screen and keeps the screen locked when the case is closed.
Best of luck with it though, I hope you find something suitable.

there are also laptop style cases, though the common type is a folio style. Where the shell - case is permanently attached to a fake leather lid and the keyboard is held in place by magnets and uses Bluetooth and micro USB for charging on some cheaper cases some more expensive cases now use USB-C.

the models I like is the laptop style where the case and keyboard detach from each other.
Examples of is style is:
zags 's rugged book and slim book.

In these models the keyboard has a hinge mechanism like a laptop but the shell for the iPad is held in place by magnets and alignment posts and can be detached and flipped around, so the keyboard is behind the iPad.

as far as I understood your query, a keyboard case with removable bluetooth keyboard works. I have had many of those in the past, the brand name is something like Fenti, not sure of the exact spelling though. The removable keyboard helps a lot, you can work far from your iPad and use a bluetooth headphones for something like 10 feet, still do not expect much quality for something around $25.

So this is the keyboard I use. It comes with a case where you can slip the bluetooth keyboard inside. It's got a magnetic panel on it so, as you use the case you can angle the screen and place the keyboard a little way out where it is kept in place by its magnets.
Now, I found the case bulky and unattractive and prefer a leather case I have from Moco, I think it was. Turns out I can slap the keyboard on the back of the iPad because both the case and keyboard are magnetic. I use the iPad in the closed form, screen down with the leather cover closed. Turns out it doesn't have to be open to work. The keyboard, as you can imagine, is quite cramped, but it basically turns the iPad and keyboard into a talking keyboard without a screen, the audio coming out of the sides. This particular keyboard has a lock key in the top right which is helpful for both unlocking the iPad but also turning voiceover on and off when I use jump desktop and remotely connect to my mac mini where voiceover is already running.
The keyboard itself isn't great quality, light and some edges where the plastic hasn't quite been removed, I think it's called fletching? Though I'm sure someone else can correct me.
Just having a quick look and I think the keyboard you might want would be this one:
https://www.amazon.co.uk/Keyboard-trackpad-Boriyuan-Compatible-Black/dp/B088NQ24W7/ref=sr_1_7?qid=1649731868&sr=8-7&srs=16143478031
to use in the configuration I suggested. This would mean you would still need a cover, but take the keyboard from this case and you can slap it on the back of it and then you have this mongrelised iPad/keyboard device. I was going to do a forum post on it as it seems quite a cool hack, especially for those of us who don't need a screen.
Hope this helps. I know the pain of trying to select keyboards whilst not knowing the orientation of how they are supposed to work or their dubious heritage. I'd recommend this solution as it's not super expensive and worth a go.

Along a similar theme, has anyone found a keyboard case that is big enough or could be retrofitted to hold a Mantis Q40 Braille display and an iPad? So substituting the typical tiny Bluetooth keyboard for the Mantis? I can't help but think this would be a fantastic duo.

Do you mean having the ipad standing up like a laptop screen in front of the keyboard? Otherwise, I imagine a pocketted iphone could serve pretty well.

A few years back I remember getting a rubberised keyboard overlay that magnetically attached to my first generation ipad mini. Though it didn't really work that well, being too cramped and not registering each key stroke, that sort of thing would be ideal. I'm still waiting for speed dots to come out with tactile screen protectors for the ipad mini 6th generation as I think it could make touch typing, if not easy, then easier on the screen itself. There is something to be said for a unified device rather than having a pile of accessories to carry about.