Well, I don't think the one I suggested was TOO crazily over budget! Just over £100 as opposed to £65 - & nicer fabric that will wear better.
Neither is my kind of thing (as I don't really do leisure wear!), but I think if you don't care about it being polyester & not wearing well or the environmental side of things, then I would buy a cheaper set somewhere else - as I don't think the RI one is worth the money.
For me, personally, I'm trying to buy less & buy better, for environmental reasons, but I am also on a limited budget. I've always been a huge fan of charity shops & fleamarkets & car-boot sales &, in the last 20 years or so, eBay, Etsy & now Vinted etc. Vintage & secondhand is my preferred way of shopping, & always has been a bit of a thing for me. And you get much better quality for your money! So I like to try & persuade people on S&B threads to consider that themselves, & if they don't want to go down the Vinted/eBay route, to at least buy better.
As I think "lounge sets" probably originated with Juicy Couture etc, there aren't exactly any vintage ones out there for me to recommend, funnily enough ...!!! So in the absence of those, I just tried to find you something in better quality, more environmentally friendly fabric.
So of course you're completely entitled to buy what you want, I was just trying to explain my own PoV & why I recommended something different. I hope none of that sounded snobbish.
Now, if you really want to feel relaxed AND look good, both indoors & out, this should impress the neighbours when you're putting the bins out ... 😁!!!