I acquired a ASUS RT-AX88U router in a business closure auction. It was in a mixed lot with a bunch of networking gear. I stumbled onto this OpenWRT forum post regarding OpenWRT firmware for this router. The original answer
That's virtually impossible, it's an all Broadcom (BCM49408 SOC, BCM43684 WLAN) design, for which no wireless drivers exist.
may no longer be accurate. I say this because I also stumbled onto this article regarding Asuswrt-Merlin (MerlinWRT or just Merlin) firmware:
Merlin is the third-party firmware available only to certain Asus routers.
Asus builds its Asuswrt using Linux via the GNU Project and shares its source code via GNU’s General Public License (GPL). Then, the Merlin group, led by Eric Sauvageau, changed the source code to create a better alternative. For free.
Perhaps the Broadcom drivers are available now and OpenWRT could support this device?
Yup, the infamous difference of "free as in freedom" vs "free as in beer".
Only some Broadcom chipsets are reasonably well supported, thanks to the Raspberry Pi foundation's efforts. In general, if it's broadcom and NOT part of a Raspberry Pi product, avoid it like the plague. Even some of the Pi products can be a bit flaky in router use cases (because the chips are designed to operate in client mode or extremely limited WLAN hotspot capability with only a few clients).