Any Markdown-based static site generator could work.

But the editor UI I think is where a lot of the power of a tool like Obsidian comes from. The main benefit for me is that it takes the pain out of cross-linking, so you can have a much more richly linked collection of notes, more like "hypermedia" than a journal.

Another option could be Tiddlywiki, which does have an editor UI but is self-contained in a web app.