Very cheap sleeve
I see people are looking for some sleeve option so I’ll share ultra cheap solution that I found - iPhone air battery case on temu/aliexpress.
It have perfect size matching X4.
Cost 1-3€. Many color options. Made with fake leather. It’s not a super quality but good enough. There’s an option with a buckle (but this one I wouldn’t recommend. The clip is very poor and it’s not needed - the device wouldn’t slide from that sleeve anyway).
Search for “iPhone air battery case”.