By default, Shopify does not provide a function to search collections themselves. If you need advanced search functionality, we recommend using an app, but if you don't need such functionality, you can customize it to search by title or handle. Here is an example of how to set it up.
How to implement collection search in the theme "Dawn"

[Implementation method] Add a search form and search result display function to "main-list-collections.liquid"

[Position of code to add] Additional code ①

[Position of code to add] Additional code ②

[Position of code to add] Additional code ③

