Follow-up from "Add the ability to cherry pick accross forks [RUN ALL RSPEC] [RUN AS-IF-FOSS]"

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The following discussion from !55970 (merged) should be addressed:

• @viktomas started a discussion: (+2 comments)

  Also (and this is non-blocking), would it be possible to set the searchTerm to '' empty string? Because otherwise, I'm worried that the user will always have to clear the default branch name to start searching.

We should clear the projects and branches dropdown filters by default.