Unify style of search buttons

[RayBB]

Following #8963 we want to evaluate unifying the styles of the search buttons with something like cta-btn cta-btn--small cta-btn--vanilla etc.

This will potentially also require changing the text input to match the height and look nice. Maybe like the button group from bootstrap here.

Describe the problem that you'd like solved

Proposal & Constraints

Additional context

Stakeholders