Aura of the Sentinel doesn't stack with Alert

The initiative bonuses don't stack.  Is this intentional, or a bug?

First of all, you should be listing where Aura of the Sentinel comes from when asking for help like this. (For anyone unaware, I found it: Oath of the Watchers Paladin from 5e.)

For others, it should apply because they're gaining a bonus of your proficiency bonus, not their own. For you, however, it's debatable. Normally, you're unable to benefit twice from your own Proficiency Bonus in the same instance. The wording of Oath of the Watchers might provide an edge case to allow it (it's a bonus, not directly adding the PB, but I'm not convinced it stacks).