No, I don’t think you are being paranoid.
Years ago my BIL spent the morning in our kitchen drinking coffee. DH (his brother), myself, and the Doberman were there the entire time. BIL played with the Doberman.
DH and I had to leave, so BIL left also. However, he forgot the tool he came to borrow in the first place so went back to our house, LoL.
The Doberman wouldn’t let my BIL in the garage for all dog biscuits in the county.
Conversely, many years later, I needed a farm sitter to feed my horses, dogs, and one cat while I flew back home for a few days. By then I had my third Rottweiler, a Lab/Sharpei, a Beagle/mix, one house cat and three horses.
In my corner was the fact the lady had her own horses, big dogs and wore a no fear t-shirt. She came 3x/day to let the dogs out and fed everyone twice daily, plus checked the horses over for possible noteworthy injuries. The dogs loved her because she came with treats, lol
You have a tough assignment and it’s probably too late to back out without leaving the owner in a real crunch. I suspect you are the only person the owner can find that is trustworthy to be a diligent home and critter caregiver.
I already gave you my best help and that isn’t much, which is leave a piece of clothing with your scent on it, at the house.
The only other thought I can think of is that when you do come in the house and the owner is not there, do not make direct eye contact with the Rottweiler. They don’t like that in many cases.
Also, when you come through the door when the owner is not home, holler for the dog in your happiest non-scared voice. Try to maintain a sense of calmness and talk to the dog in a lighthearted voice like you would greet a human.
if the dog comes to greet you or even if it doesn’t, I would not make an effort to reach out to the dog. I would keep talking to the dog and not look in its direction. Just go about the business of hanging up your coat or whatever else you’re going to do, while also keeping an eye sideways as to the whereabouts of the dog so that your back isn’t turned to him. Make sure he is aware that you’re aware he’s there, if that makes any sense to you.
It would be great if this dog has been to obedience school. That way if the dog were to come to you, you could give it the sit command and simply say “sit for a cookie”. You would have to make sure you have treats close by that you could give it some thing. Whether the dog is supposed to have treats or not I would definitely have treats on hand in your in case - this is the time for bribery.
I don’t know how to tell you to have more confidence and to lose the sense of fear that you might have with this dog. That is something that is born in all of us to some degree or another.
A third thought is that it might also help if you could spend a few nights at the home while the owner is still there. This is serious business — 8tsnot like you’re watching over two Chihuahuas and a Shitzu.
Also leave night lights on, near the bathroom and in the kitchen. To this day I leave the stove light on low so everyone can see each other.
I still, always let the dogs know if “I’m coming thru”, if they happen to be laying in my path to the bathroom or somewhere else in the night.
We have a lot of shadow in the laundry area, coming in from the garage, so I also leave that light on so the dogs can see it really is DH coming through the door, when he gets home from work. Shadowy figures are made for attacking when you’re a big black guard dog — or a red Catahoula/Pit Bull
It tKes an extreme amount of common sense and forethought to co-exist with guard type dogs. I wish you the very best, since this really isn’t what signed on for