Great! It's important to note that there is no notification support on mobile yet for tasks. It's possible on desktop.

The app is in very rapid development and it's more than a tasks app. I really recommend trying to use the normal to quickly write stuff down and create todos.

It's a fully client-side encrypted key store, mainly used for calendars, contacts, tasks, and notes. It does have a cal/carddav bridge. I use task.org for tasks, EteNotes for notes, and the android connector for native support of calendars and contacts. In GNOME it works via evolution for syncing. I use the *dav bridge for some custom integrations (like HomeAssistant).

I've been using it for about a year, and it's definitely gotten a lot better in that time. It can be a little finicky to get everything configured for the first time for a vault. You only have to do it on the first device though, then you can copy a setup URI to each subsequent device. One caveat is that if you want it to work on mobile, then you've got to have it configured with https and not with a locally-signed cert. I have it proxied through Cloudflare with a domain I use for homelab stuff.
The biggest difference is that remotely save doesn't have any kind of conflict resolution. It just overwrites the remote file as long as the local one was modified more recently. Livesync keeps separate versions of a file almost like a git repo, tracking the changes. It almost always automatically merges conflicts, but if it can't it'll pop up asking you to choose which version to keep. I have a few vaults that I share with others and multiple people can work on the same file simultaneously with no issues at all. There's end-to-end encryption built in so if you're using it externally you don't have to worry about your privacy. I write up my task list for the day on my computer in the morning, and being able to pull my phone up and check things off and have it reliably sync back to my desktop without overwrite issues works flawlessly. There's iOS, Android and Windows devices all playing nicely.

Here's a link to the docs for setting up your own server.
I'm gonna stick the docker compose and config files I used to spin mine up if you wanna use them (make sure to put them in the same directory):

docker-compose.yml

name: obsidian
version: '2'
services:
 database:
  image: couchdb
  restart: unless-stopped
  ports:
   - "5984:5984"
  volumes:
   - ./local.ini:/opt/couchdb/etc/local.ini
  environment:
   - COUCHDB_USER=username
   - COUCHDB_PASSWORD=password

local.ini

[couchdb]
single_node=true
max_document_size = 50000000

[chttpd]
require_valid_user = true
max_http_request_size = 4294967296

[chttpd_auth]
require_valid_user = true
authentication_redirect = /_utils/session.html

[httpd]
WWW-Authenticate = Basic realm="couchdb"
enable_cors = true

[cors]
origins = app://obsidian.md,capacitor://localhost,http://localhost
credentials = true
headers = accept, authorization, content-type, origin, referer
methods = GET, PUT, POST, HEAD, DELETE
max_age = 3600

Edit: Sorry for the huuuge reply, hope it's not too much haha