How do i put away my gun and walk around with just my bare hands so i can punch people? I remember doing it in the vault at the start of the game but ever since i picked up weapons i have been unable to figure out how to go back to that state since.

All i can do is lower my weapon, as soon as i hit the melee button i punch with the butt of my gun, i cant seem to figure out how to do it without a gun.

This is why we need game manuals ffs!

Go into your Pip Boy and make sure you have no weapons equipped. Then the usual combat buttons will be your punching and blocking

Hold reload to holster

Yeah, it's a bit odd they got rid of the "press hotkey again to unequip weapon" thing that was in FO3 & Skyrim. Having to go into the inventory to unequip, just so you can have a fistfight, is somewhat awkward