As far as I know, there is no place that this information is stored on. It is coded into the filesystem. However, you can manually make a list of filesystems and the corresponding precision. I would use a `case` statement to test the filesystem id against your list of filesystems. You can make the default 1 since there are very few examples where precision is less than 1 second.
Older versions of FAT and current versions of zip use 2-second timestamp precision from what I have read online. However, I suggest you fact-check that.
You can get the id of a file's filsystem with the following command.
stat -f --format="%t" $file