8GB VRAM is simply not enough, the 4060 would be a horrible purchase, especially as more games come out being first developed for consoles such as the PS5. 8GB VRAM means that games will have to be run at lower settings than necessary for the GPU to avoid having system memory get used as VRAM.
I've used as much as 13-14Gb with a 6800XT at 3440x1440 over the last 22 months (that's current and recent AAA games for that period) Sure, that's a minority of games played overall, the average usage afaik is around 10-12Gb, but not for too much longer. Newer cards with 8Gb might just suffice for 1080p now and going forward to next gen... But then again my old 1070 had been seeing it's 8Gb maxed out in contemporary AAA's at 1080p some time before 2021 (GDDR5 sure, but 6 /6X aren't multiple times faster either) and this was when knowledgeable ppl said 4Gb was fine for 1080p...
On the other hand, my gf's PC (5600X/3070 @ 3440x1440) runs many of the same games ok, 20-25 fps lower on average vs 90-100 with my 6800XT, but it is
a work first, gaming second rig. My Legion 5 (6800H/3070ti @ 1440p) gets tweaked settings and likely capped as well with AAA games to keep thermals and fan noise balanced. For that anything over 60 fps ultra and under 75-80C is a bonus. Those two examples I'm ok with lower VRAM caps due to those caveats, it's what you make of it.
For a 6800XT upgrade with some longevity and even at the same res I'd be looking at no less than 20Gb rn and for the next couple of years at least, even if only to cover as many games and optimisation outliers as possible (and numbers of the latter seem to be increasing) So only a 7900XT/XTX for now will do, with the latter having a big enough bump to be worth the price rn. The 4090, currently starting at around £500 more than the most expensive 7900XTX (which in turn matches the cheaper 4080's in price) is well out of reach. However, this 6800XT is still killing it (ditto my 5800X) so I might wait for RDNA4 and spend my pennies on useful, necessary irl stuff until then.