This was a "saving it for formal attire" premises, as I suspected I might have trouble getting served in my normal clothes. And indeed, nobody in the bar I went in to - the hotel has multiple, with the No. 27 Bars seeming to be the least formal - was dressed even vaugely like I would normally do. Chinos and a polo shirt might do it; and there were definitely people wearing runners.
However, the offering isn't stuffy - they do have an oysters menu, but they also offer burgers, toasted sandwiches and similar bar food; and a substantial tap list including multiple independent Irish offerings - Rye River are highlighted as a supplier of Irish products on their website, an element I wish more places serving tourists would do, rather than just relying on Guinness to be the Irish option on the menu.
The food isn't cheap, but also isn't obscenely priced; and the pints are actually close to reasonable - you can certainly pay a lot more in a lot less nice surroundings nearby.