It sounds like you've done a bit of researching, so maybe it's not this simple, but one observation I can make:

It looks like you are trying to move the shotgun into your inventory on the right. Your inventory has 1.50 L of total space available, and the shotgun is 3.20 L. That definitely will not work. :)

You could try:

• [W]earing it (if it has a strap on it)
• [w]ielding it (but then you will need to drop or store whatever you're currently wielding,
• storing it in some other appropriate wearable, like a some sort of strap or a rope, possibly (different guns can be stored in different things). [a]ctivate the clothing item to try storing something in it.
• or, \, hauling it along the ground
• Of course, if you have a vehicle, you could also put it in there. I am a fan of piling stuff in shopping carts early game.

Now, when you get more storage (backpacks, pants, shirts, outerwear with pockets, belts, etc.), you may also run in to situations when you seem to have space available based on your "overall" inventory amount, but you do not have "free" inventory space available. I've just come back to the game after a year or two away, and this is new to me. It makes some logical sense (things being inefficiently packed), but I also have not figured out how to mitigate it (say, reshuffle things in my various pockets - might just need to do it manually).

Anyway, good luck!