They may be on networks that cannot communicate with each other, such as an isolated guest network, despite both having internet access.
Why this happens
Being online is not the same as being able to discover another device in the room. A router can allow two devices to reach the internet while separating them from one another. Guest-network isolation is one common example, and Wi-Fi extenders or managed networks can add their own separation. The phone may browse normally and the television may play a direct app, yet the casting target can remain absent. That behavior points toward local discovery and network layout rather than the television programme itself.
Compare the actual network names and whether either device is using a guest or isolated connection. Google Cast’s setup documentation explains how AP/client isolation can prevent devices from communicating. On a network you manage, follow the router’s documentation for the intended shared-device arrangement. On a hotel, workplace or public network, do not change security controls or assume permission to do so; ask the administrator what connection route is supported. Keep a native TV-player alternative separate from casting so a discovery problem does not become a misleading report that account access has failed.
A useful way to work through it
Check the exact network used by the sender and receiver, not just their online icons.
Identify guest/AP isolation using the network owner’s documentation.
Use an approved shared-device route or a native player when the network intentionally separates clients.