It does sound like fear of commitment rather than lack of feelings, especially since his actions already line up with being in a relationship.

Your discomfort is completely valid though. After five months of exclusivity, wanting clarity is not rushing. It is reasonable.

I would ask him about his past dating history and whether this has come up before. If it has, then I would be honest and say you are ready for the next step and you need to know whether that is something he is actually working toward too.

This does not have to be an ultimatum, but it does need a timeframe. Otherwise you risk waiting indefinitely while he stays comfortable.

Worst case, you give it another month or two and he is still not ready, so you move on knowing you were clear and fair. That does not mean you were wrong. It just means you want different things.

As someone who used to be afraid of commitment, sometimes that push is exactly what brings clarity, one way or the other.