AMD Ryzen 9 5900X Processor (12C/24T, 70MB Cache, 4.8 GHz Max Boost) - £258.70 / £254 with promo (cheaper with fee-free card) @ Amazon Spain

7600x for £200 , £150 motherboard, Ram is getting cheaper, you then have a upgrade path.

This CPU is slower than your 7800x3d and your motherboard is not compatible with it anyway. Building a new system for AM4/5xxx series right now would have been a bad idea too as it's an old (albeit still good) platform. Don't feel bad (edited)

This is only worth considering if you already have an AM4 board and are productivity focussed and coming from an older CPU. For gaming a 5800X3D would be better if already on AM4. If getting a new mobo a 7600X on AM5 would be wiser for gaming only. Moreover, a 13600KF is about the same price as this and steamrolls this in single thread AND multithread, plus the mobo would take an upgrade to 14th gen Intel in future years. LGA1700 boards will support 12, 13 and 14 Gen (confirmed this week by Intel). (edited)

Unless you will be using more than the current 6 core, 12 threads you already have, I would say absolutely not. The difference between the 5600 and this will be miniscule. You'll see better gain getting a 5800X3D instead, and even that won't be that big of a difference to warrant spending £200+ on such small gains. In my opinion, of course.

Would be better off with a 5800x3D for gaming.

Depends on what you are doing. I moved to this from a 9 3900x and yes worth it. I do a lot of video/audio work and notable uplift. I’d looked at a 5950x but not worth the extra £100