Only some character models have the necessary animations to support carrying a musket. Since you claim that the "Equip" button was enabled for your character, but it doesn't work, I checked the scripts and it looks like there may be an error in the function to determine eligibility. Can you tell me the character you are playing?
Also, it may be better if you can send me a save file with that musket in inventory, because if an officer did equip it, but doesn't show the correct item equipped, that may be bugged too, so I will need to investigate an eligible character too.
In ERAS, once you give equipment to an officer, you don't get to decide whether they unequip it, so if you have a gun or sword or cuirass that you may want to use at some point, do not give it away. They decide their equipment from their inventory and for guns, they will choose based on weighted factors of accuracy, damage output and reload speed. If that calculation favors one gun over another, they will equip it and won't unequip unless they get another gun in their inventory that favors a different one.