Send view field in URL - Drupal
In replacement to your "Learn more" add "Custom text" field after "Field_program_id" in your views. In "Text" add "a" tag like

&lt;a href="/search?nodeid={{field_program_id}}" class="button"&gt;Learn more&lt;/a&gt;


Take a look in "Replacement patterns" for available fields. Read description there too for a guidance.

(this is in Drupal 8)

It is the almost the same in Drupal 7, just with [] instead {{}}. Class for "button" depends of the theme.