mysites.guru (formerly myjoomla.com) does everything you are asking for:
✔ manage Joomla websites at different versions centrally for different clients
✔ update Joomla
✔ update extensions
plus a great deal more:
✔ scan for malware
✔ restore compromised core Joomla files back to the original files
✔ automate backups
✔ uptime monitoring and alerts
New features are regularly being implemented.
You might also consider watchful.net which has similar functionality and seems to be more affordable up to 25 websites. For more than 25 websites, the mysites.guru unlimited sites option may be better value.
I am not affiliated with mysites.guru but find it useful for managing the 50 or so Joomla, WordPress and HTML websites I look after: