I figured out that the issue of being unable to toggle between HDMI and Bluetooth audio was occurring due to a browser issue. Toggling does NOT work in Firefox Nightly 91.7.0 ESR (which I was consistently using) and audio is outputted only to HDMI. When I shifted to Epiphany, it started working. I am now able to get audio on paired bluetooth headphones. I am attaching the screenshots with Epiphany (working) and Firefox Nightly (not working).
Its working even without loading graphics-KERNEL at onboot (or later) and even after commenting out dtoverlay=vc4-fkms-v3d-pi4 in config.txt.
Subsequently, I checked on x86_64. Toggling between audio streams works in newer versions of Firefox (102.0.1). So, it seems to be an issue with older Firefox versions. Wonder if there is any workaround for this..... Chromium based browsers like Brave also work properly .
Kindly mark the issue as solved.
Thanks @ Juanito for your patience in suggesting various checks. Important learning point was the need for running various startup commands to enable bluetooth in RPi