How should I clean up my laptop?

No, I didn't backup. I don't think the data on those partitions is lost, but it certainly isn't an option to format the hard disk.
 


with a iso or a persistent pendrive, you should be able to read and rescue whatever is left to another external drive as a folder
 
I think the easiest/fastest thing to do here would be to probably just reinstall Linux.

But to backup your data, you can do this with a Live CD (Linux ISO) as @brickwizard mentions.
 


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