remotely-save VS md.obsidian.Obsidian

You're not and you're actually reinventing the wheel as a couple of options for that are already available as community plugins. I've been using Remote-save for a while with a almost free private S3 bucket and encryption to sync between my computers and phone for a while.

https://github.com/remotely-save/remotely-save

It supports more than just S3 (as is listed in the README), its just what I use.

There's an Obisidian plugin for direct syncing to OneDrive that works on both mobile and desktop - this keeps you from having to deal with either triggered syncs through github or the various other, painful syncing processes.

https://github.com/remotely-save/remotely-save

I didn't try any of them to be honest. But I remember seeing a couple of posts mentioning their drawbacks. With that said, you may follow this documentation on how to connect your DropBox.

It can be done today. https://github.com/remotely-save/remotely-save

What are the specific advantages of using Remotely Save plugin compared to simply saving the vault in OneDrive?

I use Remotely Save plugin synced with a free tier OneDrive (sadly gdrive isn't supported) and it works very well. Maybe if you not find any alternatives good enought (most of then are a bit hard to setup and maintain) and do not want to pay the official sync plugin than this may work for you as worked for me.

You can use Remotely Save plug-in. It is a life saver for me to sync between different devices.

I'm currently using Remotely save without problems between Windows, iPad and Android.

My Nextcloud instance also synchronizes my Obsidian vault so highlits after uploading are available also there on desktop. On mobile I also use Obsidian with remotely-save plugin https://github.com/remotely-save/remotely-save so I have access to all uploaded files.

You might want to check Remotely Save

My Flatpak version was updated the same day. Very impressive.

I tried flatpak command line instructions as mentioned here but that too giving error

There are Linux solutions to this, macOS makes apps request permissions to important folders/ full disk access, any operating system should let you run something as a locked-down user without read/write access to your important files, etc. Installing Obsidian on Linux using flatpak or recent macOS + a firewall would let you manage a lot of the risks there, for example.

If you want simple markdown notes I recommend Paper, for to-do lists a good option is Endeavour, and there is third option, Obsidian, I don't use it because it feels complex, but maybe you will like it

Is that not this? https://flathub.org/apps/details/md.obsidian.Obsidian

It's probably best to open an issue here to ask what's going on if you're interested: https://github.com/flathub/md.obsidian.Obsidian/issues

You can check in github repo how a flatpak package is done. Here is how Obsidian is done. If you don't like any permission, you change it through flatseal app or command line. Most gnome apps and apps that follows gnome HIG are maintained by the official developers themselves. Valve, Mozilla are maintaining their respective products.