Subnet forwarding does not work in that direction. What you’ve done is allow devices in your Tailnet (i.e. your remote machine) to access 192.168.1.0/24 by using your laptop as a proxy, not the other way around; the chromecast doesn’t know it could reach your remote machine via your laptop.
This would be a giant hack and it’s unlikely to work but it’s possible you could get the Chromecast to communicate with the remote machine via your laptop by setting the default gateway of the Chromecast’s network connection to the local IP address of the laptop.
It’ll probably lose internet connection that way, not sure Jellyfin needs that (don’t think so?).
I’d rather recommend you look into getting Tailscale onto that Chromecast. I’ve never used these things, so I don’t know whether that’s possible.