Please do not block "using the website" until someone gives you access to the microphone. Simply make the parts of the page that rely on the microphone not work, and make it obvious they won't work until people give access to the devices you need access to.
And in the mean time let them browse the page as normal, instead of force-hiding the content scroll bar and presenting a full screen overlay modal. If your page explains what it's for, locking people out of that content just because they don't trust you yet is intentionally crippling the experience for no good reason.
Thanks for the feedback! We didn't realise this would pose such a problem. We've updated the website so it asks for microphone permission after people press the 'Record' button.
Thank you, that's the perfect solution. Although you probably want to offer people a way to dismiss that modal, too: it's still "waiting" for permission rather than being able to go "wait this is not what I wanted to do how do I get back to the site".
Thanks for letting us know - we've realised we were unclear with our initial correction: the modal that asks for mic permission and explains that all audio processing is done in-browser now only appears when 'Record' is pressed, so users can check out the rest of the website.
And in the mean time let them browse the page as normal, instead of force-hiding the content scroll bar and presenting a full screen overlay modal. If your page explains what it's for, locking people out of that content just because they don't trust you yet is intentionally crippling the experience for no good reason.