New cat has way more energy than resident brothers

Hi all,

Here's our situation:

• We have 2 brothers, 8y/o. Always lived together. Both very quiet, one is slightly more social with people who visit us, the other one is way more shy.

• 10 days ago we decided to introduce a 3rd cat, 2y/o male. He was rescued from a dangerous situation and had one front leg amputated. He was described as 'quiet' and 'cuddly' in the description... lol

• We're following the usual protocols - new cat has his own room, scent swapping for a few days, then cats were allowed to visit each other's rooms (without the cat), then introduced them visually during meals. We also have feliway.

• The first couple of times they could smell each other there was a bit of hissing, but nothing more than that.

• Now that they are more or less comfortable eating close to each other, we are letting them share the same room once they are done eating. Turns out the new cat is immediately ready to play, while resident cats are not. He is especially targeting the more 'outgoing' brother, tries to smell his butt and have physical contact with him. He receives just hissing in exchange, and there was even an occurrence of growling when the new cat didn't back down after the hissing.

I don't think the new cat is being aggressive, but it's clear that the resident cats are not ready for that level of energy. Still, I think the introduction went well, we never had any major red flag during the process. What would you do next? The new cat is still living in a separate room for most of the time, which is starting to become tough as he will start meowing at random times when we're not there with him.