That car seat adapter in the photo is a universal one, so you can put all the major brands of infant car seat on it - Maxi Cosi, Cybex, Nuna, Besafe, Britax, Joie, Avionaut.
No idea about the quality of the pram itself. Puggle is the own brand from The Nursery Store (which used to be Online4Baby), so it will be a business-to-business type generic make.
BTW, I would imagine that the infant car seat with this type of pram set is fine in terms of safety, if you wanted to save yourself some money on replacing it. What you usually see with those generic set car seats is that the inserts are a bit crap and don't give a great position for newborns, and sometimes the straps are tricky to adjust, but if you won't be in the car much with a newborn (aside from the drive home!) this isn't a huge problem, they do grow fairly quickly and tend to get a better fit in them by 4-6 weeks old. Also if you minimise time spent in the car seat it is also less of an issue. OTOH if you expect to use the seat a lot, including on the buggy frame, it might be worth it to invest in something more comfy and better designed in terms of ease-of-use.
Also I would be extremely wary about any car seat from a pram set sold on a less-regulated marketplace like amazon, ebay, temu, any random shopify store advertised on instagram/tiktok - there have been documented cases of unregulated car seats with those cheap travel systems. But The Nursery Store is a proper business based in the UK and (as far as I am aware) doesn't have those issues. They do trade based on price so they are prioritising cheapness over other aspects, but that's not a problem as long as legal regulations are met which it seems like they are.
Infant car seats in general are such a simple design that they all tend to get good safety performance ratings even when they are generic ones. It's the multi-stage or later stage car seats where it's usually (not always but usually) better to stick with brands where their reputation is built on quality and safety rather than price.