Going through the same issue.
Sorry if this isn’t as detailed as you’d like and you’re looking for code fixes but I’m just getting use to WP
FTP’d in and renamed the plugin directory(bwp-recaptcha_bugged) to get the website and admin to display.
This will then deactivate the plugin within the plugin page, the issue seems to be a conflict between it and potentially Contact Form 7. So time to dig out a previous version of one/both and roll back.
Oddly forms still submit without it running