Search field retains focus even when it's not shown

**Describe the bug**
Searching then going back to the front page of Phanpy retains focus in the search box even though it's not shown

**To Reproduce**
Steps to reproduce the behavior:
1. Open search box by pressing /
2. Do a search
3. Go back to the front page by pressing the back button in the browser or with a keyboard shortcut or mouse button
4. Try using any of Phanpys keyboard shortcuts, like the / again
5. Notice nothing seems to happen
6. Click anywhere on Phanpy
7. Open search with / again
8. Notice that whatever you tried to do in step 4 is now typed into the search box

**Expected behavior**
You should not have to use the mouse to get Phanpy back to normal behavior, everything should just work as normal

**Desktop (please complete the following information):**
- OS: Linux, Nobara 39
- Browser Firefox
- Version 123

**Additional context**
Thank you for your work!

Reproduce the search-and-back navigation sequence in Firefox, then inspect the search field's focus behavior when returning to the front page. Confirm the fix by ensuring keyboard shortcuts work immediately after navigation and that typing does not appear in the hidden search field.

Written by the indexing model from the issue text.