If you want to skip the noise and get to the signal of my clumsy - but working - setup, subscribe and read the detailed Steps. Disclaimer: the setup is convoluted, involved, and not extremely elegant so reader beware.
I use Nextcloud running in a Docker container on Unraid in my basement and, for the most part, it's been extremely reliable for years. I did this as part of my de-Googling process, which never ends btw. Nextcloud is a great solution for managing my 1,000's of files and contacts, my photos, calendar, notes, and tasks and it makes those accessible from all of my devices. Right now my data is in my server (old PC with some 4 TB hard drives) which is in my house so I know exactly where the bits are.
Why not just use Nextcloud Notes?
Obsidian is quite new to me and so far is pretty incredible. It's local-file focused and designed to be a tool for managing your own notes without the need of a Cloud. Obsidian does not support the WebDAV standard which is what Nextcloud uses for remote access to files.
Why not Obsidian Sync?
Obsidian Sync is a paid service which costs $10/mo or $96/yr and it synchronizes your vaults across devices with end-to-end encryption. In reality, that's not a lot of money to keep your second brain / Personal Knowledge Management (PKM) up to date across your devices.
I really want the data to be mine, all mine and not traverse anyone else's servers, even Obsidian's. I trust myself and I don't want my data to leave my home. In reality, I may switch to their Sync once I trust them or if my poor person's sync solution annoys me too much.
Why not use an Android WebDAV sync app?
I tried a few of the Android folder / sync apps that support WebDAV and none worked well with Nextcloud. One I couldn't even connect and the other didn't allow me to sync a specific folder nor actually sync individual files. I could likely debug and continue but I was lazy.