Does the HP U32 4K HDR Monitor have built-in speakers?

No. Built-in speakers are not listed in the manufacturers specification page for this monitor. "HP U32 4K HDR Monitor Product Specifications" https://support.hp.com/us-en/document/c07721979.

A review of this monitor by PCMag lists "Lacks built-in speakers" as a Con against the monitor. https://www.pcmag.com/reviews/hp-u28-4k-hdr-monitor

The monitor does have a 3.5 mm Audio Jack (Audio Out) which can be used to connect external speakers.