I want to record activities via my vivomove luxe watch but the only activity within the options is run. How do I add the other activities to my watch menu?

There should be for sure walk and run, as those cannot be removed. I'd try first to reset the watch, especially if you have recently update the firmware (it is done automatically through the Garmin Connect app, so it may have happened without you even knowing it).

You can also try to go to Device Settings -> Activity Options and tap "Edit" in the upper right corner. A screen will open that allows to add/remove the activities to be shown on the watch. You can have up to six loaded on the watch (out of 11 available), including Walk and Run that cannot be be removed and are always the first two.