Nah they have infant carrier seats with rotating bases as well now @Lochroy . Cybex started it but all the brands are at it now.
OP - you are looking for one of the cheaper brands which have a car seat that has a rotating base option. For example Graco with the Snuglite, which can go onto SnugTurn, or Kinderkraft - anything with i-Lite, which can go onto the Endura rotating base, or Joie i-Juva with Encore base.
Or you look at popular brands of car seat, often included in bundles, where the rotation base isn't generally included but can be purchased fairly cheaply, e.g. Maxi Cosi/Joie.
Joie's Encore base takes all their current infant carriers (i-Juva, i-Snug, i-Gemm, i-Level, Sprint) and is £190 which is more expensive than the others here but does go on offer for £150-160 ish fairly regularly, just not right now.
Sprint is also worth considering in its own right considering the isofix is built into the seat itself so needs no base.
Maxi Cosi Familyfix 360 is on offer for £135 currently and takes the Pebble 360 Pro, Pebble 360, Coral 360 or Cabriofix S (but not basic Cabriofix i-size).
As bundles go I'd be tempted by this if I was buying now. I think the same company has it listed for £250 on ebay. Not sure if that's a major red flag or not. https://www.amazon.co.uk/dp/B09ZLVP6ND/
Beware of the totally unknown brands who only trade through amazon or similar. Their car seats (and prams) are sometimes counterfeit and don't meet safety regulations.
The other way you can do it is look at which pushchairs can take a car seat - not in a bundle, so including travel type buggies for older children - and then combine with the cheapest combo of infant seat (with universal adapters) + rotation base which is probably currently Cybex Cloud G in last years' colours with the Base G. There are sometimes some good Maxi Cosi offers too.
The other idea is to go for second hand pushchair, new car seat.
You also may want to consider whether rotation is truly necessary in the car seat? In some ways I find this gimmicky, because an infant seat doesn't really need a rotation feature. The fact it comes out of the car means you can rotate it any way you want when it's not on the base. Rotation is helpful for the second stage but many of these seats already have the rotation built in for much less than you'd pay for the toddler seat + extra cost of rotation base for baby seat. Worth considering anyway.