PC Speaker just means a piezo buzzer on the motherboard, many early DOS games use it for music and SFX.
Looking at your motherboard, I can't see one soldered on.
The official Compaq Maintenance and Service Guide says:
"An external speaker must be installed into the speaker output connector to hear audible beeps during POST."
In other words, Compaq routed the PC speaker beep signal through the audio chip to the Speaker out on the back panel. No onboard piezo and no 4-pin header to connect one. So if you're using a discrete sound card like your Soundblaster 16, there are no POST beeps, and no PC speaker is available.
90s PC: IBM 6x86 120Mhz. 128MB/6GB. ATI Rage Pro 3D.
Boring modern PC: R9 3900X, RX 7800XT. 32GB/1TB.
Fixer upper project: NEC Powermate 486SX/25. 16MB/400MB.