Be sure to test the power supply before going too far down the rabbit hole.
deadite9
You should be able to sign in to just the store app by clicking a tiny little box on the subsequent window that pops up during the sign-in process. That's how I sign in to the store for app downloads without having to use those same credentials to sign in to the PC.
That box is intentionally made small and easy to miss because they obviously want you to use a MS account across the whole machine, but it's there if you move slowly and look for it.
That said, you shouldn't have to sign in to download any app updates from the store. You can also download new apps without signing in-- the license will just be tied to the machine instead of your personal account if you do that.
This unhelpful error is just MS being MS. Best option is usually just to leave it be and check back later, as it oftentimes really is a problem on their end.
I'd definitely take the opportunity to make sure the BIOS is up to date (just to be sure you're running one that supports the newer CPU), or just default everything if you're already on the current version before pulling the 5600G and dropping the new one in. Then after you've confirmed the board recognizes the 5700X3D it's just a matter of changing your settings back and dialing in the memory timings.
I know it's tedious, and probably not strictly necessary, but I figure it's better to start off with a clean slate whenever you swap out a CPU or reconfigure your memory, just so something you didn't think about doesn't come back to bite you later on.
I usually just go through all the BIOS screens where I've made changes and take photos with my phone, then use those as cheat sheets to refer back to.
FYI unless you're planning to manually tune that memory to a lower speed, DDR5@6800 isn't really feasible on AM5 at the moment. 6000MHz is the current sweet spot, and even getting that stable is much easier to achieve with 2x16GB modules.
Should work fine. You'd just have to set the timings manually to run them all @3200 (one XMP profile runs at 3333MHz, while the other is set to 3200, even though the main timings and voltage appear to match otherwise). Or if you didn't want to bother with setting everything up manually you could probably run both with the second profile, which is 3000MHz on both kits.
Four sticks is usually harder on the memory controller than two, but you wouldn't be pushing high clocks on the memory anyway, so you'll probably be fine. That said, a new 32GB kit would be simpler in the long run, even though it's cheaper to just add a second kit.
X570 or B550 would probably be your best bet if you wanted to stay with AM4, and X570S (no chipset fan like the original version) would be ideal if you can find a board. I really liked the Crosshair VIII Dark Hero I ran for a while, but it's not particularly cheap.
As for minimizing RGB, MSI usually includes a physical switch on the board for turning it off-- in addition to the software switch in the BIOS-- if that seems appealing. ASRock also lets you manage very basic RGB settings directly in the BIOS if you just want to avoid installing extra software.
If you move up to AM5 you'll need a new board, CPU, and RAM... so that route could be pretty expensive. That's the route most would probably recommend, though, instead of investing more in an older platform.
Current Intel isn't really worth it for gaming, and 13th/14th gen honestly aren't worth the worry/headache.