Toggle On/Off inventory input key (E) gets disabled along with the character movement input when I open the inventory

Use “Set Input Mode Game and UI” instead of “Set Input Mode UI Only”. If you want to prevent the player from moving when the inventory is open, the best approach would be to make one Input Mapping Context for gameplay, and one for UI. Remove the gameplay MC with “Remove Mapping Context”, then add the UI one with “Add Mapping Context”. Reverse the process when you close the inventory.