Just thought I'd mention this for others to find. I recently enabled ECDSA certificates for my domains and discovered that Unifi controller didn't work. The solution was simple.
Simply add the following to /var/lib/unifi/data/system.properties
and restart your controller.
unifi.https.ciphers=ECDHE-ECDSA-AES256-GCM-SHA384,ECDHE-RSA-AES128-GCM-SHA256
unifi.https.sslEnabledProtocols=TLSv1.3,TLSv1.2
I've tested this on a Gentoo server with Unifi-6.5.45