To increase the size of your inventory, you need to unlock and use the backpack in Hytale. The backpack is a separate item from the default inventory, but its sole goal is to give you more slots to put items. Fortunately, the backpack is unlocked fairly early on in Hytale, as all you have to do is upgrade your workbench to tier two.
I generally like using the Peak Design backpack, except that bringing it on vacations means that I have to leave my handheld(s) at home. It's not wide enough to accommodate even the original Switch once things are stuffed into its side pockets. The Vortex 1.0, on the other hand, let me bring both my Switch 2 and Steam Deck, thanks to its two dedicated handheld sleeves. It's also wider and taller, which means its top zipper compartment can hold a 16-inch laptop and a tablet.
The Porter Frame series was quietly discontinued by Yoshida & Co. due to its embodiment of a design approach becoming increasingly rare: the courage to say no.