I realise I’m replying to myself here (lol) but I thought I’d give an update as I’ve worked out the solution.
What I did was I went into Settings (in the Chrome extension) and Excluded Domains. In there I found that somehow, github.com was added in. I simply deleted this entry and refreshed the GitHub login page. Now when I selected Sign in With A Passkey, BW responded by prompting for confirmation of the stored passkey. Voila! Login worked perfectly.