It will require a BIOS update but it will work just fine.
As a matter of fact, it specifically lists the Ryzen 7 5700X3D in its CPU support list.
ASRock AB350M CPU Support List <-click here
The R7-5700X3D is third from the bottom of the list. The TDP isn't listed but I know for a fact that
the TDP of the R7-5700X3D is 105W and there are literally twelve other AM4 CPUs with a TDP of 105W that are supported by this motherboard (including the 16-core R9-5950X). The board itself has the full 8-pin CPU supplementary power connector which means that it would be quite suitable for overclocking (which makes sense because it's a B-series board and only A-series boards don't support overclocking).
One thing to keep in mind however is that X3D CPUs don't overclock so they're not power-sucking monsters. In fact, the reason that they're so limited is because excessive heat can easily damage the 3D V-cache (and there have been instances where this actually happened).
The Ryzen 7 5700X3D doesn't actually draw that much power when you compare it to other CPUs in its performance class:
"The Ryzen 7 5700X3D consumes a peak of 117W, an impressive 100W less than the Core i5-14600K that it actually beats in gaming workloads (but trails in productivity applications). Notably, this is much lower than the theoretical PPT (peak) of 141W for AMD's 105W TDP rating."
I mentioned the R9-5950X earlier and while it also has a TDP of 105W, it's power peak is far higher at 141W:
As long as you apply the proper BIOS update (the latest one), I cannot foresee any problems with this motherboard using an R7-5700X3D. The one thing that might hold you back in gaming is the fact that 300-series motherboards only support PCIe3. Having said that, if you have a PCIe4 video card that has an x8 or x16 connection, you shouldn't have any issues. To put it simply, if your video card isn't a Radeon RX 6400 or RX 6500 XT, you'll be just fine.
Once, just for fun, I tried my R7-5800X3D on a
Biostar A320MH motherboard to see if there was a performance loss in gaming compared to my ASRock X570 Pro4. I dropped the resolution to 720p to ensure that my RX 6800 XT wasn't bottlenecking anything. I had no lack of faith in its power, but I wasn't sure what effect PCIe3 might have on it. I can attest to the fact that CPU-wise, the performance wasn't hampered in the slightest by that A320 board, a board that is considerably lower-end than your ASRock AB350M. In fact, the A320MH only had a single 4-pin CPU supplementary power connector but it didn't matter because X3D CPUs are clock-limited and won't draw more than a 4-pin can provide, especially not in gaming.
You'll be more than fine with that board, I guarantee it.
😉👍