You can absolutely sync your vault without a paid subscription. Simply save it within your OneDrive or Google Drive folder. Alternatively, you could use Syncthing if you prefer a self-hosted solution.
You can, but _you_ need to figure out how to do it.
If don't know how or can't be bothered, you can pay for Obsidian Sync - which Just Works.
I tried to roll my own syncing with syncthing and iCloud and Dropbox. In the end I spent so much time debugging and dealing with files clobbering each other mid-sync I figured out $4/month to support a project I use daily isn't too much.
Zero problems since and I use Obsidian regularly on 4 different devices.
Seconding this. I use Obsidian and Obsidian Sync for personal stuff, but my employer doesn't allow Sync, so I use Obsidian very happily as a standalone on my work computer. The work vault simply never gets exposed to the outside world (we don't allow USB memory devices either).
https://obsidian.md/blog/free-for-work/