Floor like in a hospital and then at least felt very thin sounds somewhat like linoleum.
Linoleum doesn’t have to be bad in itself.
But that’s ultimately not the point.
Floorboards or tiles
You probably can’t lay the tiles without first removing the -unknown- floor. I don’t know click tiles, that has to be said, but with the small area I imagine it wouldn’t be so easy without preliminary work.
Tiles are also very cold in the shadow and in the transition period.
If the sun shines on them, they are certainly also very warm to hot or too warm to stand on barefoot.
For me, tiles would therefore be the second choice.
Floorboards. Basically, a lot of wood is suitable here, and there are many impregnation options. Also, a lot of color options are possible.
There are "fully" impregnated floorboards. These are not just painted but impregnated throughout. Might be interesting for a snow-covered surface for sure.
I don’t have personal experience, but I have heard that the protection can be such that it is "indestructible."
Then nothing would probably gray or silver, meaning color stable.
But you would have to find out more yourself about exactly what that is.
Otherwise, larch is certainly suitable; it is a durable wood for outdoors.
Bamboo might also be interesting here.
Presumably, the current floor wouldn’t necessarily have to be removed for wood either, depending on the situation, e.g., the build-up height at the terrace door.
Since the weather overall strongly affects your balcony, I would, if strong impregnations are not suitable/possible/unwanted, rather choose a somewhat darker shade. Otherwise, a light one will probably become unsightly very quickly.
