I got one of these recently and I’m pretty happy with it. It’s a repurposed iPad screen, 2k, 4:3, and put into an aluminum frame. slightly larger than your requirements tho. Got the version with usb-c and mini-hdmi inputs, and is USB powered. https://www.aliexpress.us/item/3256801503431249.html
In the vein of multiplayer games with singleplay bot matches like Battlefield 1942 being mentioned, try the standalone mod for for Battlefield 2 called Forgotten Hope 2. Many maps have single player bot support (by launching coop server on your lan). Battlgroup 42 mod for bf1942 has a tons of singleplayer maps too. You can also get bots via third party plugins for the og Day of Defeat (sturmbot or shrikebot) and as mentioned Day of Infamy has built-in bot support. Worth mentioning are the Arma 3 WW2 mods and dlc.