I got this error in cPanel hosting account, where there was no problem with disk quota (for account). After some time, I found that the cPanel tool "Select PHP version" was installed on v7.1, but several WordPress diagnostic tools found that v5.6 actually works, and they also found problems with the file system.
The File Manager tool in cPanel showed that all permissions were correct and the folders were writable.
One of the diagnostic tools I used was part of the Wordfence plugin. It was available in the "Toolbar" menu in Wordfence> Tools> Diagnostics (tab).
I reported this problem to the hosting company, and it seems to have fixed itself (the person who answered my support request indicated that he had not fixed anything). I think this was probably a symptom of a problem that affected several hosting accounts, and someone else at the hosting company probably discovered this and fixed it.
In case others run into a similar problem, I hope this answer helps them spend less time trying to find it. As soon as I found that the wrong version of PHP was working, I realized that this was probably not something that I could fix with cPanel access only.
Highly irregular
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