One additional note — when I have both plugged in, and I unplug the one being recognized, it immediately recognizes the other one and applies whatever screen settings I had set on the now-unplugged monitor to the other one, suggesting it thinks it’s the same monitor plugged back in.

Yes: FB21777337

Unfortunately the duplicate binary EDID issue is a known, common practice among monitor manufacturers - they'll often use the same binary edid for a full batch of monitors to cut on complexity or cost. Asus does not offer a tool that can let me patch this on the monitor, and I couldn't find a DIY solution that lets me patch it myself. I'm 100% certain both monitors were plugged in. I've replicated this again just now to get you a new sysdiag as well. It's worth noting - I am dropping the monitor to "1920x1080 (low resolution) @ 30Hz" specifically to mitigate the risk that it's a bandwidth issue. It's also worth repeating that when I disconnect one monitor the other one is immediately recognized and connected, and it adopts the profile of the first monitor (i.e., it adopts the 1920x1080 @ 30Hz setting, which is non-standard for this monitor), which makes me think the system believes they're the same monitor. Also, worth repeating that if I plug in a Apple Studio Display ("5K Retina") and one of my monitors, it detects both of them successfully. Anyhow, I've replied into the bug report via Feedback Assistant with a new sysdiag result attached.

I gave Asus' DisplayWidget Center a try, but as far as I was able to tell, it does not offer a way to directly configure the resolution of the monitor. The monitor's menu doesn't offer any such options either. BetterDisplay has options that supposedly override the default resolution and the native resolution of the monitor in the OS profile, but I couldn't get that to make a difference either. I tried a HDMI 4k @ 120Hz EDID Emulator as suggested earlier, and this finally worked. Starting from both monitors plugged in, I unplugged one cable from the monitor, connected the EDID Emulator, and plugged it back into the monitor; the MacBook didn't detect the monitor at first. But unplugging the other monitor made it detect the one with the emulator, and then re-plugging in the other monitor detected it as well, and so both monitors were working from there on out. I now have both monitors running at "3008x1692 HiRes @ 120Hz" (which I understand is, in practice, 3840x2160 pixels being pushed to the monitor at 120 Hz). It's still unclear to me what the root cause here is - whether it worked because the EDID Emulator provided a sufficiently-different ID (which in fact it did, totally different numeric serial number, display name, vendor and model ID, etc.), or because the EDID Emulator forces the signal to 4k @ 120Hz. It seems to me like the MacBook Pro should be able to detect both monitors "out of the box" though - I imagine the expected behavior when plugging in the monitor is that the system can detect it, and push it a supported resolution that the system can handle.

I think I follow your point - however to be clear, I had already dropped the "working" monitor down to 3008x1692 "hiDPI" @ 120 Hz (which from what I looked up online, is 4K @ 120 Hz in terms of pixels being pushed to the screen by the MacBook), and connecting the other monitor into the MacBook Pro at that point still had no effect, until I added in a EDID emulator into the second monitor and then connected it. So the "working state" where the MacBook Pro has one monitor connected at 4K @ 240 Hz isn't the true "starting point," and I believe even with HiDPI enabled the refresh rate is changing when I change it in OS settings, because it's a very visible drop particularly down from 100+Hz into 60Hz or 30Hz. Additionally, I've tested the "working state" where the one working monitor is at e.g., 1920x1080 low-DPI at 30Hz (very blurry due to low DPI, very visible framerate skips when moving the mouse around due to 30Hz) So presumably this working state would allow the second monitor to be plugged in with plenty of headroom, but it still only starts to work when a EDID Emulator is added into the second monitor.