Bach is universally considered a Baroque period composer, meaning that he lived earlier than composers like Mozart and Haydn, who are considered to be Classical period composers.
This was long before the Romantic period. The general idea of Bach’s music is rather mechanical, precise, mathematical, without the extreme amount of feeling and emotion that we hear about 100 years later. However, this is extremely misleading.
In fact, this piece in my mind is one of the most intimate and expressive things he ever wrote. The period is “Baroque”, but the feel to me is highly romantic.