u/Puzzleheaded-Cake261

Hello! First post here, looking for some insight/advice on introducing two cats.

Our resident cat is a neutered male, turning 6 years old this month. We recently moved from my parents house into our own house this past year, and my parents had a handful of cats there that co-habitated with our resident. He was alright with most of them, pretty disinterested, but would try to play with them on occasion, but one cat that passed this past year was the only one that he would tolerate in his own space. (Sleeping near each other, play-fighting, chasing, etc.)

Flash forward to moving into the new house, we noticed small behavioral changes in our resident (more vocal, very clingy towards us, etc.) and we thought that he might miss the companionship of another or other cat(s) when we are at work.

We found our new introduction at a local shelter, a ~7 month neutered male. He's an absolute sweetheart, took to his new room when we brought him home like he had lived there already. We went through the scent swapping with some washclothes, site swapping, no hissing there, just some mild interest from the both of them. After a few days of this and underdoor interactions (only one hiss that we can recall, other than that just some swiping) we moved on to introducing a babygate for them to smell and see eachother through. Again, mild interest, new cat was more interested in getting over the babygate than the cat on the other side. Resident would come and go, but still, no hissing from either party.

After a few days of this, we removed the babygate entirely, and they seemed pretty okay. They both will tolerate one another to be in a window at the same time to look outside, they'll sleep on opposite ends of the couch, there are just times where the new cat will walk about the house and our resident will stalk behind him/chase him, and once the new cat is cornered, the resident will just sit and stare at him, or on occasion will bat at him (no claws, just thumping his head usually.) The new cat will cower and pin his ears back for the most part, with an occasional hiss if the resident doesn't back off. They haven't had any full-on fights, no claws, blood drawn or yowling, just these tense standoffs that end with the new cat scampering off under the bed or into the room we had initially set him up in, or a few whacks to the head from our resident.

We're just wondering if this is okay to allow them to continue doing? Should we be separating them again? Do they just need to get through this stage? (It's only been a little over a week now, which we realize isn't that long all things considered.) To be frank, our resident is a bit of a spoiled diva, and I wish the new cat would set him straight with a few thumps of his own, but I think the size/age difference makes it a bit intimidating.

I'd appreciate thoughts/experiences/advice, just wanting to be sure that this is alright for the both of them in this scenario!