Problems logging into Apple TV on older small tube TV

Modern devices require a TV that has an HDMI port. It would also need support for HDCP (to transmit copy protected content via streaming services). There will never be a guarantee when using a converter and functionality can cease at any time. Any converter that aims to circumvent copy protection would not be authorized and would be against the law.

You stated in your original post that you are using a tube TV (otherwise known as CRT). That would only have analogue ports, whereas an Apple TV box or any other streaming device would require a digital HDMI connection.

The only way to connect to that display would be through a converter. If you were using that it would not be a supported method, and while it may be working fine now it could cease at any time. The core functionality of the device is also to stream content and most of that is copy protected, which requires transmission through HDMI via HDCP. That would not be possible through a converter and any that circumvents that would not be legal.

If you made an error then providing make and model of the TV will verify whether it has an HDMI port.

I can view Apple TV fine on this TV, it is asking me to re-log in and because I cannot scan the QR code or read the multi-character code because it comes over too small to read, I am asking for some sort of other alternative to log in.

You might want to be more specific about the devices in play (make and model, for example) and how they are connected.