cannot get older apple tv to sign in on tv

If you have the Apple TV box, then you can connect that to your TV through HDMI, and set your TV to take input from that HDMI port.

Apple TV HD, tvOS 16

Is that the “older” Apple TV that you wanted to inquire about? It seems up-to-date (tvOS 16) to me.

Or is the question about a different model? If so, which one?

Identify your Apple TV model - Apple Support

Find your Apple TV model number - Apple Support