After updating Minecraft to the newest version, I discovered this issue while using one of my add-ons that I have created. Further testing showed that this issue affect items from my other add-ons, but interestingly did not affect any vanilla items.

The effects and recreation of this issue is very simple. Using any custom item with the minecraft:cooldown component will trigger the cooldown, which correctly stops the item from being used again until the cooldown is over. However, the cooldown overlay does not appear, thus removing any indicators for when the cooldown is finished. Changing the format version of the items' files did not appear to fix the issue.