This tool is so expensive. I want to use it but for this to be an alternative to Notion you'd have to pay for Sync and Publish, which would come to $24/month. That is very pricey for many people.
While I encourage supporting the Obsidian team by paying, there are ways that you can get the same features without paying.
Sync - On iOS, you can use iCloud to sync your files between your Mac and iPhone. I imagine that there are more configuration options for this on Android.
Publish - lots of different ways to deploy your notes to a site. There's one repo that helps you publish with Mkdocs [1], and I'm sure there are other tools the community has created to solve this problem.
It may not be as simple to set up as Notion, but that's the price you pay for wanting a solution to be cheap, private, and let you own your own data.
Realistically if you care about privacy and owning your stuff you'd go with one of the many open-source options. Especially if you have to bring your own syncing anyway.
If you put your notes in a Git repo you can make a pipeline that deploy your notes online using a static site generator and e.g. GitHub pages. Of course Sync/Publish is smoother and easier, but don't let the price of Sync/Publish stop you from trying Obsidian itself (which is free for personal usage).
Obsidian is free, and you can bring your own syncing and publishing.
You can choose to sync via pretty much any sync solution like Dropbox, iCloud, Git, etc. For publish you can static site generators like Jekyll, Hugo, etc.
It's just reading/writing a directory of files. If you set it up to save into a synced directory, whether that be Google Drive, OneDrive, iCloud, Dropbox, whatever, you can point all your Obsidian installs on various machines to the same synced directory and it'll give you the same effect.
Logseq uses Markdown files for all of your pages and journal entries. However, it doesn't support nested directories, choosing to embed "%2F" in the filename instead. That is quite ugly. The only thing Logseq doesn't use Markdown for is configuration files, AFAIK.