In virtualized environments (whether on-premises or in a cloud), trying to boot the virtual machine from an external boot media can sometimes be difficult.
In such cases, it might be easier to disconnect the virtual disk(s) from the failed VM, and connect them as additional disk(s) to another, working VM instance, and then use that instance to recover your data.
While it's technically possible to recover after a recursive chmod from the root directory by first using the package management tools to restore standard permissions to system files and directories, and then going through all the remaining files and directories manually, it might not be the most optimal use of your time and effort.
Restoring from a full backup would definitely be easier and faster; depending on the complexity of the software installed to the cloud instance and the level of automation you've created for your cloud setup, even a full reinstallation might be.
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