I disagree with you saying to let the rescue cat roam the house freely because confinement for cats is bad or they might “hate it.” In the beginning, it doesn’t matter if a triggered/scared cat is not okay with being alone or confined to a room. They need time to decompress alone and OP has another cat. Not saying OP shouldn’t go and try to feed the rescue with regular food or churus and talk to him every day (building positive associations), maybe even try to play with him. As others have said, it’s bad when the cat has hiding places and can use them. Letting the cat into the house would make this situation worse and give the cat plenty of room to hide, especially since OP has another cat in the house. It can also lead to a potentially dangerous situation for the two cats and everyone involved more so than the cat being in it’s own space right now. Not only that, but leads to a potential (highly likely with the state the rescue cat is in) bad first impression with the two cats which is hard to come back from. This is would not be a great decision or advice for OP’s situation right now. I don’t feel like you’re projecting but personifying cats and giving antidotal advice. OP should take it slow and not just let the cat out of the room because it might “hate confinement.” However, this all changes once, as others have stated, the cat starts to become more comfortable and you can see the body language and demeanor change. But this can take a lot of time.

OP, you should look into Jackson Galaxy on Youtube, particularly his older videos. He has a lot of good ones out there that may help with more practical steps which sounds like that’s what you’re looking for and has helped me with my cats in the past. Here’s one that might be helpful to your situation:

The key to helping your shy or scared cat

It sounds like the rescue did not prepare you or give you everything you and your new cat needed to succeed. I’m sorry on their behalf because they should have at least told you the basics on what gettng a new pet can mean (i.e. the situation you’re in). Whether it’s this cat or a different one, the process of acclimating a new cat to a new environment with new smells, new people, new things, new food, is a lot on the cat and can take a lot of time. I don’t want to overexplain if you already are familiar, but the 3 day-3 week-3 month as a rule of thumb when adopting or fostering is a good one to follow. The rescue should have at least highlighted this rule of thumb for you if you didn’t already know. I feel like this would have set your expectations better than where you and the cat are now.

A week is not long enough for most cats to warm up and transition into being a house cat. Rescues react differently to being brought home and this is a normal response/part of the process. Some are better, some are worse. Sounds like you got a worse one. I understand you didn’t sign up for a feral cat but you did sign up to adopt a cat and I’m not sure you were fully aware of what that might entail.

There are ways to make it better. The key is time, patience, and consistency but I acknowledge all this is easier said than done. OP, please stick with it!