Adding custom link text to a URLInputButton

I think the solution is clearer, and already hinted at in your attributes

1. Add a new input for the text, and set its value to the btnText attributes value, allow it to update that attribute on change
2. when you set the URL, don’t use (post && post.title) || 'Click here' instead use (post && post.title) || props.attributes.btnText so that it falls back to the existing value
3. give the attribute a default value of Click Here when you register the block so that it starts out with that value

This way you could use a TextControl, or even a richtext to allow italic and bold etc. Then you can use a toolbar button to trigger the link the same way buttons and hyperlinks do.

Note though that if you just want a button that links somewhere, you can use a core/button block or core/buttons. This would save time, allow some limited user control, and improve theme support by letting global styles control how the buttons look from theme.json.

If you just want a button that looks different, you can also register a block style or block variant to allow users to pick alternative stylings