There are a few loserbenchmark.... ahem... I mean userbenchmark entries of your Prime b350-Plus board running with a Zen 3 CPU. These are with the most recent Beta BIOS versions with AGESA 1.2.0.7 or 1.2.0.6b.
I don't think Intel's ADL is on the table for you because of how well the R7 5800x3d handles games. Intel can only match the Gaming performance of the 5800x3d with their flagship offerings, which is beyond your specified budget. There's no reason to jump to ADL if your board can handle a 5800x3d. Other processors like the 5700x or 5900x are also good picks. Here in the USA, the R9 5900x is only $92 dollars more than the 5700x. I don't know what prices are like in your location but here in the USA the 5900x is a better value than the R7 5700x and 5800x offerings.
The only question I have is what kind of 1440p monitor are you using? If you're gaming on a 60hz or 75hz monitor then you probably won't see much of a benefit in upgrading the CPU. With the R5 3600, you shouldn't be having too many issues with a Game that doesn't challenge the CPU like Metro Exodus. Also, it wouldn't hurt to check your cooler, temperatures, and per thread CPU usage before upgrading. The 5800x3d, 5900x, and 5800x don't run as cool as the R5 3600, so you may need a new CPU cooler as well.
DDR5 prices have come down a bit since it first came out late last year. AMD seems to be hoping that DDR5 RAM will be even cheaper when Zen 4 comes out later this year. At some point in the future, DDR5 prices won't be a factor but that might take a year. Personally, if I was going to jump to a new platform, then I would wait until a few months after Raptor lake and Zen 4 come out, otherwise I would pick up a Zen 3 CPU. Jumping to an Intel platform also would require you to take care of your Windows key because of a new board and a new CPU cooler.... and on top of that your motherboard isn't worth much these days and your R5 3600 is maybe worth $120usd at the most.
