Hide file tree browser tooltip stays open for an unusually long period of time

Context

See #582189 (comment 2934657391)

Hide file tree browser tooltip stays open for an unusually long period of time

Environment: Production, Browser: Chrome 142 / Arc, OS: macOS, Viewport: Desktop/Tablet, Screen Reader: None

Steps to Reproduce

1. Navigate to a repository with the file tree browser closed.
2. Click the file tree browser button to open the file tree browser (desktop and tablet viewport sizes).
3. Notice that the Hide file tree browser tooltip remains open (due to the focus on the file tree browser button). The tooltip does not go away until you interact with another element on the page. This is unnecessary and distracting.

Expected vs Actual

• Expected: The tooltip is only shown if the user hovers over the file tree browser button.
• Actual: After the file tree browser button is clicked, the Hide file tree browser tooltip remains open until the user interacts with another element on the page.

Evidence

Desktop viewport	Tablet viewport
desktop.mov	tablet.mov

Additional Info

• Console errors:
• Reproducibility: Always