The type of car seat which is compatible with a pram (travel system) is called an "infant carrier" - it's usually fairly lightweight with a handle, and is used from birth up to anywhere from about 6 months to maybe 18 months, depending on your preference, how big your baby is for their age, and the model of seat, as they are slightly different sizes.
The infant carrier seat straps into the car using the seatbelt, or you can buy a base for it which usually attaches using isofix (those are clips in the car designed for attaching child seats, all modern cars have them).
After they grow out of the infant carrier, you usually install a seat in the car which stays in there and just lift the child in and out.
All infant carriers even the cheaper/more basic ones tend to get a very good safety score when tested, the only thing to be aware of is counterfeit seats, which you're unlikely to come across unless you're after a knock off version of a very pricey seat e.g. Doona, or if you're looking at the very cheap "3 in 1" type prams only sold online through tiktok/instagram etc - avoid those.
Unfortunately, it’s not against the law to sell car seats that would be less than useless in a crash
This is not true. Although some of the car seats sold for older children get dubious crash test safety scores, it's not less than useless - any car seat that meets legal regulations, used properly, for the age/weight/etc of child it's designed for, is better than nothing in a crash, and better than the seatbelt alone. Any rear facing seat, again used properly, is highly protective, and all infant carrier seats are rear facing as babies need to travel RF until a minimum of 15 months (but preferably longer than this!)
So you can just get whatever infant car seat comes with your pram, with no worries at all as long as the pram is a proper brand which meets UK regulations, then replace it with a longer lasting one later, and at this stage look more into the safety testing etc.
Or, you can buy the pram and then check what car seat adapters it has - the vast vast majority have the option to use "universal" or multi-brand adapters - if it says it takes Cybex, Nuna or Maxi Cosi these are those. With those you can buy any infant carrier seat from those 3 brands, also Britax, Joie, Avionaut and Besafe and a few other brands go onto those adapters. That means you could buy a cheaper infant carrier than the ones included with the bundle, or you could get one with features you like e.g. longer lasting, or better positioning for newborns or more lightweight for example.
Or, you can get some of the fixed in place seats which are suitable from birth, and not bother with a seat which goes onto the pram at all. Personally, unless you use the car very little, I think it's helpful to have an infant carrier/lift out seat especially when they are tiny, they sleep so much that it's easier not to have to disturb them every time. Plus, the fixed seats often cost about £100 extra to get the version with a newborn insert, and you can get a cheaper infant carrier for less than £100, so it sometimes doesn't make financial sense to do this.
Most prams which work as a travel system tend to be bulky/heavy, and have a fairly small seat, so won't be comfortable to use all the way up to age 3/4 anyway. Most people use the big bulky system for the first year or two and then swap to either a lightweight smaller folding buggy, or a larger forward facing only buggy with a bigger seat, for use with an older child - these don't usually take the lie flat carrycot, and may not take a car seat either.