Partner suggests that you are sharing your lives together, usually a home, parenting, exchange of finances to some extent. This isn't sounding like a mutual partnership, more of a casual boyfriend/ girlfriend which is fine if your expectations and aspirations are in the same league. From OP's information so far and the usage of "DP" in this context, I'm wondering if there is a mis-match with OP presuming more commitment and "DP" presuming a more casual boy/girlfriend situation.
DH and I consult with each other over our plans, primarily for information to ensure the DCs are looked after, also to ensure that we are not compromising the other. It's very rarely an "ask permission" in that we would veto the other for anything other than practicalities.
If you haven't arranged to meet, then you are free if you're not living together. Chatting about deviation from normal routines is normal conversation, but not a major thing.
The alarm bell for me is not chatting about the planning of a holiday. That's quite a major social arrangement to omit. DH went on holiday with friends in our early months. It was discussed and informally planned by the time we got together and booked shortly after. I didn't go as it didn't fit with my term dates. The key thing was that it was openly discussed. Many years later when we were living as partners I had a holiday opportunity that didn't work for him, but it was all openly discussed.
Have you actually discussed your long term aspirations together. 2 years is quite substantial when one party behaves in a casual way, and the other uses phrases like partners and assumes more involvement. Normally its a stage when futures are being planned and if moving in together isn't on the cards, it's normally for a transparent reason.