Differently to how most emotions work in irish "Ta brón ar" usually means he is sorry, "tá sé brónach" (he is sadness essentially) is the more common way of saying someone is sad. This can be done with other emotions "athasach" and "eaglach" for example, theyre usually a very expressive form though, "tá eagla ar" usually means hes scared whereas "tá sé eaglach" would usually mean overcome with fear. With "brón" these two forms have a particular distinction, but ejth most other emotive language theres very little distinction, but the "Tá _ ar" form is more commonly used
The adjectival forms (brónach, áthasach, eaglach, srl.) are usually only used as attributive adjectives (an fear brónach - "the sad man", amhrán brónach - "a sad song"). When English uses an emotion as a predicative adjective ("the man is sad") Irish generally prefers to use the noun construction tá brón ar an bhfear.
"is sadness on him" is just word-for-word translation. Irish syntax is different to English. It's VSO https://en.m.wikipedia.org/wiki/Verb–subject–object
You are confused about two structures using tá and ar: "Tá ar+X VN" where X is a subject and VN is a verval noun means "X must V", while "Tá N ar+Y" where N is a noun and Y is a noun means "N is on Y" ,and in the particular case of Y being a subject and N a feeling (like sadness or joy), it means that "the feeling N is on Y" which will be further and correctly translated in "Y is A" where A is the adjective correspinding to the feeling N.
Examples : Tá air snámh = He must swim. Tá brón air = Sorrow/Sadness is on him = He is sorry/sad.