https://www.amazon.com/Compatible-tomtoc-Protective-Hardshell-Accessories/dp/B07HCZ6BN5/
You'll need either something fat like this to hold the grip case.
Or something flexible that can stretch to fit everything you need.
Although that second one is uglier than sin.
A zipper sleeve case would do just as good.
https://www.sfbags.com/collections/gaming-cases/products/slip-case-for-nintendo-switch-lite
The whole sling/messenger bag recommendation is simply due to most cases not being very functional for anything else. You can spend $20 -$40 on something specifically designed for the switch. Or you could spend $25 - $50 and get something that works great for the switch and other things too.