Limit calendar block to show specific category

The Calendar Block cannot do what you are looking for by itself.
https://wordpress.org/documentation/article/calendar-block/

I am not aware of any plugin that allows the case you are looking for. There is something like that for events – but not for posts.

I see 2 possibilities for you:
a) You look for someone who writes an extension for the block. You can find someone like that here: https://jobs.wordpress.net/
b) You write your request to the Gutenberg developers. Maybe they will add the desired function in a future version: https://github.com/WordPress/gutenberg/issues