iirc browsers used to allow direct filesystem access.

They never did, if anything it's the opposite in that I think there are now APIs that can make this possible.

With TiddlyWiki you had to essentially File -> Save As and save the HTML back over itself. There were other ways too but they were all workarounds to the issue that browsers don't allow direct access.

They did back around 2008. I used Wiki on a stick - see https://stickwiki.sourceforge.net/which was kind of neat) but after a few years, Chrome etc stopped letting it save itself.