Improve search UX on Branches page

See thread: !172873 (comment 2220430054)

Problem

Branches page (https://gitlab.com/gitlab-org/gitlab/-/branches) has 4 tabs: Overview, Active, Stale and All.

When user searches by a branch name on any of these tabs, GitLab automatically redirects the user to All tab.

Screen_Recording_2024-11-19_at_10.21.00

Proposal

Allow to search by branch name on Active and Stale tabs without redirecting to All tab. Scenario: the user wants to check if the particular branch is stale or active.

Open question

How should it work on the Overview tab?