Move code in `user_defined_plan.rs` to the `extending-operators` doc

From the intention: https://github.com/apache/datafusion/blob/main/datafusion/core/tests/user_defined/user_defined_plan.rs#L18-L24, I think it's better to put the code in examples.

Also, the code isn't solid, and its tests are fragile, such as https://github.com/apache/datafusion/pull/15744#issuecomment-2811894336.

cc @alamb

Read the intention in datafusion/core/tests/user_defined/user_defined_plan.rs at lines 18-24, then inspect the extending-operators documentation and the referenced PR comment about fragile tests. Done means the relevant code has been moved into documentation examples and the test fragility concern is addressed or clarified.

Written by the indexing model from the issue text.