How to deploy multiple search-fields?

Hello and good day to you ??

I want to place different search-fields on different pages:

1. Blog-Archive
2. Support-Archive (“Support” is a custom post type)

so whenever the visitor enters a query on Blog-Archive, then only blog-articles are being displayed underneath the search-field.

Whenever the visitor enters a query on the Support-Archive page, only posts from this custom-post-type “Support” will be displayed.

Is this something that can be achieved with your plugin?

If not, could you please recommend about how to deploy a solution for this (for non-coders like me)?

Thank you in advance
Sascha