Okay - so that tells us it expects to be using https. We've ruled out the most common cause of that error that I know of. As I mentioned, I'm not very familiar with how HA configures Node-RED, so I don't have an obvious next step for your to try.
Perhaps someone more familiar with Node-RED in HA can help.
I've tried multiple browsers on different devices (Win10: Chrome, Edge, Firefox, Vivaldi; iOS: DuckDuckGo, Safari).
I've tried direct connection on local LAN with HTTP and HTTPS
https : // 192.168.3.87:1880/ gets the “ERR_SSL_VERSION_OR_CIPHER_MISMATCH” response
http : // 192.168.3.87:1880/ get "The plain HTTP request was sent to HTTPS port" response
I've played with installing NGINX SSL proxy this morning - not resolved the issue.
Tried to create new SSL certificates - installed "Let's Encrypt". Failed to generate new certificates as it can't get to HA:
Hint: The Certificate Authority failed to download the challenge files from the temporary standalone webserver started by Certbot on port 80. Ensure that the listed domains point to this machine and that it can accept inbound connections from the internet.
The behaviour's the same whether I access remotely (your-host . duckdns . org) or locally (192.168.3.87). So it feels like an SSL/certification problem in HA/Node-RED?
Sadly considering whether to do a complete RasPi/HA/Node-RED rebuild - reluctant to do that as I don't understand what's changed and gone wrong this week?