I was wondering if anyone could identify the manufacturer of these chess pieces, or possibly the name of its design (beyond just "Staunton". It's correct I think, but want to know more)
This is beautiful set, and a nice photo. I imagine it is a family heirloom that has gained a nice patina from much use. It looks very much like one of the original sets from the 1800s by Jacques of London and I would go to their website. https://houseofstaunton.com
In the early sets, rather delightfully, the rooks had a small K or Q symbol engraved inside the turret, so that, in the manner of the time, you could write the score as "Kings Rook at the adverse Queens Bishops square, giving Checkmate"
It's design is called Staunton, named after chessmaster Howard Staunton (see here: https://en.wikipedia.org/wiki/Staunton_chess_set).
This chess set is the FIDE official recommended one for tournaments.