RI-7542 Rework the visuals of the inline search for the hash/list keys in the browser

[valkirilov]

Description

Rework the visuals of the inline search for the hash/list keys in the Browser page, to make it look less broken after the EUI replacement:

• make the search input fill the available width
• bring back the "onBlur" behavior that should close the search if you go away without typing anything

Before	After

How it was tested

1. Open the Databases page and connect to an existing database (or establish a connection with a new instance)
2. Go to the Browse tab from the main navbar
3. Execute the following commands in the CLI, to setup some seed data that will help you verify the changes
4. Now, you can open the seeded keys and click on the Search icon in the table

HSET myhash field1 "value1" field2 "value2" field3 "value3"
RPUSH mylist "element1" "element2" "element3"

Before	After

Close the search input on blur

Additionally, I bring back an old behavior that was temporarily deleted for some reason:

• when clicking outside of the search field, it will hide if if there is nothing entered inside it
• and it will stay visible if you have search value applied

Screen.Recording.2025-09-26.at.14.23.15.mov

[github-actions]

Code Coverage - Frontend unit tests

St.❔	Category	Percentage	Covered / Total
🟢	Statements	82.16%	20033/24382
🟡	Branches	67.53%	8687/12863
🟡	Functions	76.3%	5336/6993
🟢	Lines	82.58%	19613/23749

Test suite run success

5161 tests passing in 677 suites.

Report generated by 🧪jest coverage report action from 11f9866

[ArtemHoruzhenko]

lgtm