What does "proverbial man with a hammer" mean in this context?

Proverbial means “referred to in a proverb or idiom”. The proverb referred to here is “To a man with a hammer, everything looks like a nail” (variants include “He that is good with a hammer tends to think everything is a nail”). The overall meaning is you should not get so fond of a given tool (programming language, or pattern) that you use it exclusively, regardless of whether it is fit for the job at hand.

There are various claimed sources of the original quote, but wikipedia attributes it to Abraham Maslow in The Psychology of Science.

It is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail

A related idea is the golden hammer, meaning an instrument that is so admired it is used for everything. This is regarded as an anti-pattern.