Yes, they do. I exported blog content from our current Squarespace site, and imported that content into my local development WP and remote site (Azure). I see that for local site, the Most Used tab in the dashboard Menus Categories section contains all the categories. However, for the remote site, there are only the four categories including Uncategorized, even though I changed the Default Post Category in Settings > Writing to Environmental (by the way, the picker there sees all the categories). I deactiveated Yoast SEO plugin as that was activated remotely, but not locally where all categories show in Category widget on blog page.
It is perplexing …