Refactor(filtered search): share filter module

What does this MR do?

This MR moves the (now tried and proven) filter store module to be shared with the filtered search component. This allows others to use the store module with their implementation of filtered search.

Screenshots

N/A. This MR moves code around and therefore has no visual difference.

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry
• [-] Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• Separation of EE specific content

Availability and Testing

Not much risk involved with this as it just makes some files more available.

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers
• [-] Informed Infrastructure department of a default or new setting change, if applicable per definition of done

Security

If this MR contains changes to processing or storing of credentials or tokens, authorization and authentication methods and other items described in the security review guidelines:

• [-] Label as security and @ mention @gitlab-com/gl-security/appsec
• [-] The MR includes necessary changes to maintain consistency between UI, API, email, or other methods
• [-] Security reports checked/validated by a reviewer from the AppSec team

Related to #232465 (closed)