A regular capture card will adhere to the HDMI DRM HDCP, which means it'll only record a black screen. As you guessed, there're capture cards which either don't implement HDCP (unlikely for major brands), or which have been hacked and can be flashed with custom firmware.

I've read OBS on Windows also only records a black screen, at least with hardware encoding enabled (NVENC, AMF, Quicksync also implement DRM as part of the driver). Software encoding might work.

As always with content: If it's on your device, it can be copied.

PS: Now I remember Crunchyroll also uses Widevine, but I've seen it streamed over Discord. So either Widevine L3 doesn't prevent recording, or it doesn't work in Firefox, or Discord doesn't use hardware encoding on Windows (unlikely), or something in my comment is wrong information -> Disclaimer, I'm just repeating from memory what I've read.