Thats different though, 6nm was a "free" upgrade from 7nm since the porting of 7nm designs was straightforward with no additional investments required to port a 7nm SoC design to 6nm. Cost wise a SoC on 6nm was equal or cheaper, by the time Sony switched to it yields were probably good enough to produce cheaper SoCs compared to 7nm.
For 5nm they need to invest in porting the PS5 SoC to it plus the added wafer costs of 5nm itself probably didn't make financial sense to do so
Just to make sure by "4nm" you mean N4 and N4P which are just 5nm with efficiency, performance and slight density improvement?
If so cost shouldn't be much different, they are 5nm still and the design cost similar, by 2024 yields should mature to the point its a no brainer considering its modest improvements in performance (11%), efficiency (22%) and slight density (6%) increase.
3nm on the other hand seems very unlikely for 2024 even though
TSMC are targeting 80% production capacity late 2024 would be pleasantly surprised if they do but rather not get hopes up
While true R&D is mostly* done by AMD the cost of said R&D is passed on to the cost of SoCs AMD sells to Sony, so if the R&D is higher the cost of the SoC would be higher for Sony. AMD doesn't sell its chips at wafer costs they have to recoup R&D investments and make some profits as well.
*We know from previous Cerny interviews for PS4, PS4Pro and PS5 that Sony works with AMD in the design of the custom SoC to add features and remove some that aren't needed and some of those features make it to AMD off the shelf products and some don't
That being said considering RDN4 is rumored to be used only for midrange i suspect the RDNA4 card we see on the market will be a by product of their work with Sony for PS5 Pro much like the RX 480 and the RX 6700 (non XT). IF RDNA 4 releases next year I assume we'll see a similar situation with Pro using a cut down version (i.e 60CUs vs 64) of the off the shelf card.
That why I find the RDNA 3.5 rumors odd unless there's no RDNA 4 next year and AMD just launches a improved (RDNA 3.5) mid range card based on the work (RT HW) they did with Sony and with the RDNA3 bugs fixed