Is the reason there's no 'yn' in this sentence because its predicate is a prepositional phrase?
Yes. No need for yn/wedi with a prepositional phrase like that.
Dw i mewn penbleth - I am confused
Mewn gwirionedd - In reality, in truth.
Mae'r siop ar gau/ar agor/ar osod/ar werth/mewn llanast - The shop is closed/open/to let/for sale/in a mess
Have a look at the Tips and Notes for the "Work" skill - https://www.duolingo.com/skill/cy/Work :
Many building and workplaces are also feminine and are introduced with mewn, meaning in a. The difference between yn and mewn is that yn is a very specific place, whilst mewn means any old place and in a. Yn is also used when saying in the (yn y).
Along with some examples.
Sorry, that's not my question. I'm asking about the particle 'yn' that usually appears in sentences with 'bod', not the preposition 'yn'
"Oh, really? What role did you get?" No, you idiot! I mean I'm in the middle of a play right now! Go away!