There are two menus that pop up when you hold down “Q”, you might be only looking at the bottom menu. There is a menu on the top that contains wearables, such as the jetpack.
If you click here, it’ll hide the bottom menu on your screen:
The bottom menu is only for placing or selling items really, so you won’t be using it at all to equip things like jetpacks. You’ll be using only the top menu for that.
Jetpacks are considered a wearable, so first you need to go to the top of your screen and click this button to go to the Wearable Hot Bar.
After that you’ll find a button here for your jetpacks:
Now you’ll drag the jetpack into one of the wearable hotbar slots to use it.
Yeah in that last screenshot you’re still looking a the weapons tab. You need to click the button that says Jetpacks to see your jetpacks. Or alternatively the one all the way to the right that says All.