What is this plant, and is it a perennial or just a temporary visitor?

This is catmint, Nepeta. The leaf shape, grey-green colouring and blue-violet flowers fit this type of spreading perennial well.

Yes, it is perennial. It can look a little sprawling or tired after flowering in late August, which is normal. It overwinters in the ground and produces new shoots the following spring.

To tidy it now, lightly remove spent flowers, but avoid hard cutting back late in the season in Västernorrland, Sweden. Leave more substantial tidying until spring, when you can see what has survived winter.