Hi @ZaLiTHkA and welcome to the community 
Exporting from the password manager will only include individual vault items or collections you have canManage permissions for when an organization has been selected. More information about individual vault exports can be found here.
For a full backup of an organizational vault, you’ll need to go into the Admin Console and export from there.
The desktop or browser extension have been limited to exporting individual vaults. With the next version (2024.6) it will have the same capabilities as the Web Vault (password-protected exports and export of managed collections). I announce this here
The current mobile apps do currently not include the fields you mentioned. This is something we are aware of and have planned to have fixed with the rollout of the new native mobile apps.
Logging into the CLI with admin privileges and exporting an organizational vault is the same procedure as logging into the Admin Console and exporting.
I hope I was able to shed some light on the issues you’ve mentioned.
Kind regards,
Daniel