Just downloaded the appimage again which is now version 1.6.7 but still has the same problem as described in your question.
I think I found some kind of safe solution now. I extracted the appimage and installed the extracted files in /opt/Obsidian. First we're going to extract the appimage:
~$ /home/mook/Obsidian-1.6.7.AppImage --appimage-extract
Now we move the extacted files to /opt/
~$ sudo mv /home/mook/squashfs-root /opt/Obsidian
We want to have the files owned by root:
~$ sudo chown -R root: /opt/Obsidian
We fix the permission for the sandbox file:
~$ sudo chmod 4755 /opt/Obsidian/chrome-sandbox
Some subdirectories are only accessable by root due to permissions, this prevents the application from launching, we need to fix that too:
~$ sudo find /opt/Obsidian -type d -exec chmod 755 {} \;
Now we can start the application:
~$ /opt/Obsidian/AppRun
2024-07-31 06:43:51 Loading main app package /opt/Obsidian/resources/obsidian.asar
Ignored: Error: ENOENT: no such file or directory, open '/home/mook/.config/obsidian/obsidian.json'
2024-07-31 06:43:52 Checking for update using Github
2024-07-31 06:43:52 Success.
2024-07-31 06:43:52 Latest version is 1.6.7
2024-07-31 06:43:52 App is up to date.
The application launches without complaining about permissions. I'am also able to start the application via double-click on the AppRun-file in my file manager or via menu-entry after creating a .desktop-file.
Security note:
Since we are running an executable which is owned by root and has the setuid-bit set the executable will run with root-privileges which could be considered a security issue as well. We only should do so if we trust the application. But at least the application runs sandboxed.
For me this was a temporary solution which I don't use any longer. Instead, I use an apparmor-profile now, please see my other answer.