When do we expect that would be?
Some of the newer AMD APUs like the HX 395 have insane performance, but in exchange a high price and high TDP. Steam Deck's APU is an interesting compromise because they went with Zen 2 for better battery life, fewer cores in exchange for a bigger GPU, while pulling in RDNA 2 to make a really compelling offering at a good price. I can't see what comparable compromises they could make right now to pull off the same thing.
Valve supposedly picked up the custom Aerith chip for cheap because Microsoft failed to use it. Most of AMD's off the shelf APUs, even the handheld optimized ones like Z1/Z2 Extreme, offer too much CPU and not enough GPU, or are memory bandwidth starved for the GPU.
Strix Halo is being shoved into handhelds right now. It starts to pull ahead in performance around 20-25W. That isn't too bad but is too high for Valve who are prioritizing battery life. Cost is the other factor. It's debatable whether Strix Halo actually costs much to make. It uses a "big" graphics+I/O chiplet next to small CPU chiplets.
If they go custom, your imagination is the limit so let's do that.
On CPU, they can push to 6-8 cores but use the more compact, lower-clocking variants. There's Zen 6C, but there's allegedly also a Zen 6 "LP", which would be the analogue to Intel's LP E-cores. We don't know if there are any compromises in this core, or even confirmation if it's real. But if it can at least match the low clock speeds of Steam Deck (3.5 GHz turbo), then you could get an improvement from increasing core count to 6-8, higher IPC, and possibly AVX-512 (for some emulators) if that support remains intact. AMD LP cores should have 2-way SMT, no problem there.
An idea MLiD is pushing is that 8 CUs of RDNA4 could outperform 16 CUs of bandwidth-starved RDNA3.5. So if RDNA4, or an RDNA4.5 mobile-focused variant, or RDNA5/UDNA1 are on the table, a low CU count could perform better than you might expect. I think RDNA4 or newer is essential, to ensure FSR4 support which AMD may never backport to RDNA3/3.5. Standard RDNA4 may never be used in an iGPU, but we should have a clearer picture of that within 6-12 months.
On the bandwidth front, LPDDR6 may offer a wider memory bus with fewer chips, but I'm not sure yet. One thing that has been missing from many AMD APUs has been Infinity Cache, which can help to increase the effective bandwidth. As little as 16 MiB could be sufficient for 1080p.
Something similar to the leaked AMD Bumblebee (2x Zen 6 + 2x Zen 6C + 2x Zen 6 LP + 2-4 CUs RDNA4) or AMD Sound Wave (ARM-based with 16 MiB Infinity Cache) is what I'd expect, but with stronger graphics.