Please explain, in practical terms, what you think the difference is between something that is equipped and something that is in your inventory. What does it mean for something to be equipped?
For me, something is equipped if and only if it is in your hand. Everything else is in your inventory. That bow on your back is in your inventory. The only slot that seems reasonable for a lit torch is a hand - otherwise you are burning everything in whatever bag you put it in.
5e already has rules for switching between weapons. Every turn, you get one free object interaction. This can include something like drawing one weapon or stowing one weapon. If you want to do more than this, it takes a full action*. So, if you're holding a bow and you want to switch to a longsword, you have the following options:
1) Turn 1: Take a shot with your bow (action). Stow your bow (free object interaction). Turn 2: Draw your longsword (free object interaction). Attack with your longsword (action).
2) Turn 1: Stow your bow (free object interaction). Make an unarmed attack (action). Turn 2: Draw your longsword (free object interaction). Attack with your longsword (action).
3) Turn 1: Drop your bow on the ground and draw your longsword (free object interaction). Attack with your longsword (action).
4) Turn 1: Stow your bow (free object interaction). Draw your longsword (action). Turn 2: Attack with your longsword (action).
*The dual wielder feat will allow you to draw two melee weapons as a single object interaction.
This seems like a granularity that isn't all that practical for a video game, but it might inform an actual cost for switching weapons in combat.
