Use a specific snippet factory in tests

What does this MR do and why?

Contributes to #494689 (closed)

Problem

We are going to add a not null constraint for snippet fields project_id and organization_id. This change breaks test factories that generate invalid records without any of these fields.

Solution

Update test suite to use a specific snippet type (Project or Personal) instead of a generic snippet.

In a follow-up merge request I'm going to remove snippet factory completely.