I think this is mildly instructional as many domestic cats suffer minor injuries to the bridge of their nose. Domestic cats are inquisitive. They like to sniff objects to discover what they are. They like to force their head into small spaces sometimes as part of this inquisitive behaviour. This can only result in one potential; a scratched nose or a minor injury.

When I first fostered my cat as a young kitten, he was a full-time indoor cat. When he became a young adult he wanted to get out. The windows were old-fashioned with a latch. They were single-glazed and they swung upwards. He lifted up the latch and forced his nose under the window and wriggled out. This was a heavy window. He scratched his nose. No surprise there.
The point is made. Cats’ noses do take a bit of a hit sometimes. I am not a vet but there is nothing to worry about when this happens. However, my motto for injuries and infections which don’t look too bad with which the cat coping well is to watch and wait. See how things develop. But do it with vigilance and regularity. Prompt action may be demanded.
Any sign of things going wrong, take her to the vet quickly. If things clear up; fine. The health scare is over.
The picture on this page prompted this short post. The Reddit user and owner writes:
“I returned home from vacation a week ago, and noticed my cat has a dark discoloration of some sort on the bridged of her nose. I was gone for 2 weeks, so I have no idea what happened. Appetite, bathroom, socialization habits are all normal. Anyone have any similar experiences? Thanks in advance!”
It looks like his/her cat, being alone from their human caregiver, behaved a little recklessly. Perhaps she was agitated at the loss her human companion. Her behaviour was a little rash and her nose was injured. I am guessing of course.
Below are some more articles on injuries.