Big Sur won't automatically boot from external disk
One solution that worked for my desktop iMacs is to reset the PMU, which I accomplished on the iMac by powering off, unplugging from the wall point, and holding the power button for some seconds before replugging and powering up again.
Today I came across the same situation on my MacBook Air 2015—completely ignoring the Alt key and also ignoring the Startup Disk setting—so I reset the PMU on the MacBook Air by the conventional means. That fixed the issue, the Alt key worked to display the Startup Manager. I've noticed this behaviour coincides with a change to the startup sound, which now sounds more raucous and far less sweet. I presume that some recent update has tinkered with the firmware.