As far as I can tell, the 4 replaced the 3. So while I wouldn't be unduly concerned about differences in performance, you might want to find out the date of manufacture for the 3's.

And maybe try and get the tyres you want somewhere else?

I ordered 4 Primacy 4+ tyres (205/55 R17 95V) from ATS and are due for fitting this Saturday, only for them to call back and said they could only get the Primacy 3 and I will not be charged any extra for that. Is it worth waiting for them to get hold of the 4+ or should I just go with 3? Is there much difference between the two?

The main difference will most likely be the wet weather performance and mpg (probably one rating letter better for the 4 over the 3), with possibly some smaller benefit in noise and wear.

Personally I'd ask for a significant discount (you are getting old tech and they likely bought them well before any inflationary increases), but would not accept any tyre that was over 6 months old, but then I do low mileages and thus need mine to last a long time in years.

Some people say (pun not intended) than 2 years is still ok, but the problem for me is how / where they have been stored (temperature, in sunlight, part of the tyre bearing weight that it shouldn't leading to it being mis-shapen), which could make a difference to how long the tyre lasts and susceptibilty to premature failure.

The tyre manufacture date is on the sidewall and is given as week number / year, e.g. 52/22 is the 52nd week of 2022, i.e. the end of December last year, etc, etc.

Given the huge recent increase in potholes, many tyre fitters have (at least round my way) have been doing a roaring trade and thus I would be surprised if any had much long term stock unless it was so old that no punter wanted to touch it with a bargepole.

It could be that they've been hanging around for a long time as that tyre size combo isn't very common - a shame it wasn't the very common 205/55 R16 91V, where prices would've been far lower because of much higher demand and competition. Quite often less common tyre size combos mean that you have less choice because the wholesalers supplying the fitters don't carry much stock.