I did a deep dive on TiddlyWiki recently. No, it doesn't need a server; an entire site can be self-contained in one HTML file.
If you want to run it as a multiuser, web accessible wiki, it runs on top of NodeJS.
ETA: Wikipedia has reminded me the feature was called UniversalXPConnect, and it was a Firefox thing and wasn't cross-browser. It still sucks that it was removed without sensible replacement.
TiddlySaver.jar was one such workaround. A check in the Wayback Machine suggests that it was originally required only for Safari, Opera, and Chrome; IE and Firefox needed no such plugin. Nowadays, there are several workarounds, and setting up one is a mandatory installation step: standalone applications, browser extensions, servers, etc. Some are clunky (e.g. you have to keep your wiki in your Downloads directory or the browser can't write to it), and either way, TiddlyWiki is no longer truly a single stand-alone HTML file, at least not for writing purposes. It's still a very versatile tool, though.
I thought opening index.html in the browser was basically just a demo.
It is a common gotcha that new users will lose some of their work while they learn persistence.
The other mode is with a nodejs server (it's what I'm using). This allows me to access the wiki from all devices.
I forget that File -> Save is even a thing for websites.
You have to click a save button in the app, and it will generate a valid copy. However, most users deploy some plugin or software which allows transparent auto-saving.
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.
So I'm trying to understand the difference, the payoff. I understand that local web APIs are ass and you very quickly run into the need for a server.
But I'm wondering about the utility of combining the two approaches. It seems like a contradiction in terms. Here's a server to help you with your dev setup oriented around not needing a server.
I guess the main win would be cross device access? You have it online and you can edit it easily.
I'm editing my stuff on my phone in a text editor. And syncing it to my laptop with a sync app.