I have to ask... Why a Pistol length gas system?
Please, no offense intended at all.... but..
The reason you can't find a lot of Pistol length 10.5" 223 Wylde barrels... is no one really uses them.
Tons of 10.5" barrels run fine with a carbine length gas system.
that said...
Criterion barrels ( as well as others ) makes quite a few options in .223 Wylde, 10.5" carbine length gas, chrome lined.
https://criterionbarrels.com/product-category/ar-15/223-5-56/?v=00dc5da36527Criterion barrels have been very accurate for me. They are well respected, and probably produce the most accurate chrome lined barrel out there.
Given the cost of ammo.... the slightly higher price for a Criterion barrel, is a huge bargain.
You can buy a lesser barrel and shoot up the difference in costs, in just a few mags of ammo, just trying to make the cheaper barrel shoot to your expectations. Lol