How to add a search button in my sites Google SERP's?
It can be added through structured data.
How do you propose I do that? I know nothing about SEO and these things.
If you don't know what to do then you just have to hire someone to do it for yourself.
And if you are unwilling to do that then you have to learn it and do it yourself. There are several tutorials for it, along with youtube videos just make a search for it and you will find plenty of data.