Ok, that suggests it’s probably not related to file permissions. I think it’s most likely to be their mod_security rules - to find that out (or rule it out), raise a support ticket with your host. If it is mod_security blocking the upload, they should be able to whitelist the offending rule/s. They will probably want to know your IP address, the time the 403 error occurred and the URL that caused the error.
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Moodle 3.8 - Error 403 when attempting to inset an image
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