How to determine which capability to use?

Not sure is that a rule or just something that happens to work that way, but most of function that take capability as argument also accept roles in same argument.

If I am not mistaken passing lowest role you want to grant access ('author') should work for that role and upwards. Please test before use.

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Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)