If I needed a budget build, I'd probably look in the direction of used parts on AliExpress, you can sometimes find good deals on AM4 CPUs (that platform had a lot of longevity, even now my main PC has a Ryzen 7 5800X) and for whatever reason RX 580 GPUs were really, really widespread (though typically the 2048SP units). Not amazing by any means, but a significant upgrade from your current setup and if you don't get particularly unlucky, it might last for years with no issues.

Ofc there's also the alternate strategy of going for a mid/high end rig and hoping it lasts a decade, but the current DDR5 prices make me depressed so yeah maybe not.

I genuinely hope that at some point the market will get flooded with good components with a lot of longevity and reasonable prices again in the next gens: like AM4 CPUs, like that RX 580, or GTX 1080 Ti but I fear that Nvidia has learnt their lesson in releasing stuff that pushes you in the direction of incremental upgrades rather than making something really good for the time, same with Intel's LGA1851 being basically dead on arrival, after the reviews started rolling in (who knows, maybe at least mobos and Core Ultra chips will eventually be cheap as old stock). On the other hand, at least something like the Arc B580 GPUs were a step in the right direction - competent and not horribly overpriced (at least when it came to MSRP, unfortunately the merchants were scumbags and often ignored it).