I grew up in a home with 7 cats, and now own two sweet kitties of my own. I have experience as a foster carer for cats, including shy cats that need a bit of care and trust, and for kittens. One of my cats is quite skittish and shy, so I have experience with more timid kitties and what they need to feel safe.
If you want your cat to stay at my house, I have a dedicated room for my foster cats / cats I am pet-sitting. They will have their own quiet, calm space, and a nice window to look out of, so they're not overwhelmed by a new environment (and no risk of them finding the perfect hiding spot and becoming invisible). If you have multiple cats, I can fit up to two in that room comfortably. I will keep your cat separate from mine for their comfort and safety, unless it's longer stay where there's a chance for them to get used to each others scents and get to know each other through the door before meeting. I like to spend a few hours a day in there with the cat to keep them company, get to know them, give them scritches, keep them company, and play with them (I'm fantastic at playing with cats).
If you want me to stay over at your house, to keep the cat in their normal surrounds and routine, I am happy to do that.
I can also drop by your place to feed the cat, scoop the poop, refill water, and play and snuggle with them. I can do this at the same time each day so the cat can anticipate when someone will be entering their space, and reduce their stress, and continue their routine. I will snap all the photos and videos of your kitty to send you, to help when you're missing them and reassure you that they are getting lots of love and attention.
I work from home and have a flexible schedule....