Why isn't the BIOS' ROM chip made using CMOS technology?
You're mixing up implementation technology with colloquial terms for functionality.

CMOS - Complementary Metal Oxide Semiconductor - is a method of making logic and related circuitry using both N-Channel and P-Channel field effect transistors.  One of its defining characteristics is extremely low static power consumption - power is almost only used when changing state.  As a result, a CMOS static memory chip can retain its contents for years on a battery, and is a handy place to store semi-permanent information.

BIOS and related startup code has traditionally been stored in PROM or EPROM devices.  EPROMs in the era of the IBM PC were typically made in pre-CMOS technologies like NMOS, but the critical distinction is that these were not typically writeable when installed in the computer, but only in a special programmer.  Further while many contemporary systems and clones used EPROMs, the actual production versions of the IBM-PC used cheaper non-reprogrammable PROMs (pinouts were typically compatible in use).

The PC-AT design then added a battery backed CMOS memory for storing customizable settings, and also (perhaps in the same device) a persistent real time clock.  This came to be colloquially referred to by end-users as CMOS, though it was of course only a particular usage enabled by a then rapidly spreading chip technology.

Today of course we no longer use parallel E/PROMs for BIOS, but rather use serial NOR flash and transfer the contents into faster RAM for execution.  Modern FLASH chips are in fact made of CMOS-derived technologies.  And they typically can be reprogrammed in circuit.  It's really up to the system designer if they want to put semi-permanent configuration information in a battery backed RAM, or in reprogrammable flash - the end user or post-boot operating system may have little actual visibility into a distinction.

But even if flash is used for settings, there's still typically going to be a low power real time clock that keeps running on battery.