To avoid using pavucontrol I want to use commands to change HDMI audio to jack headphone and vice versa. Under Raspberry Pi OS it runs nicely.

Under Raspberry Pi OS Bullseye:

pactl list | grep "Active Profile" gives:
Active Profile: output:analog-stereo
Active Profile: output:hdmi-stereo

Changing from HDMI audio to jack headphone:
pactl set-card-profile 1 off
pactl set-card-profile 0 output:analog-stereo

Under Slackware-arm 15:

pactl list | grep "Active Profile"
Active Profile: output:stereo-fallback
Active Profile: off

The version of pactl under Raspberry Pi OS is 14.2, Slackware-arm 15.0.

My impression is this is not useable. How could it be accomplished?

"pacmd set-default-sink 2", assuming the headphone jack is index 2, works here on a pi 4.

I have tried sink 0 till 23. The only time I did not see the message "Sink x does not exist" was for 0 or 1, depending on audio was set on HDMI or headphone jack.

On mine, "pacmd list-sinks" shows 3 sinks available, 0 and 1 are HDMI and 2 is the headphone jack.

Mine gives as output only index 0

I know that you're trying to avoid using pavucontrol, but you might check it to see if all 3 profiles are available. If they're there, enable all 3 and you should be able to use cli to control outputs afterwards. Works for me, anyway.

-set both profiles to stereo in pavucontrol
-reboot
-pacmd list-sinks -> No PulseAudio daemon running, or not running as session daemon.
-mplayer "something"-> I hear "plof'
-pacmd list-sinks | grep index
* index: 0
index: 1
-pacmd set-default-sink 1 -> swithes HDMI audio to headphone jack
-pacmd set-default-sink 0 -> swithes headphone jack to HDMI audio

Thanks Netcrawl!

Remark: Don't use pactl (as in Raspberry Pi OS Bullseye), but use pacmd.