docs: refine public README badges and release links

[hpark3]

Change Type

• Bug fix
• New feature
• Documentation
• Refactor or maintenance

Summary

Refined the public README presentation for the .public.viewer-saver release snapshot.

Changes included:

• reduced badge clutter by keeping only the most useful badges
• removed lower-signal badges such as build passing and Maintained? yes
• kept Contributions welcome and aligned the badge set to a cleaner 5-badge row
• added a Releases link so users can find the latest public build more easily
• moved the Releases link into the Live Demo section for a more natural placement

This makes the README feel cleaner and helps users find the right download location without overloading the top section.

Related Issue

Fixes #

Testing

• Tested locally
• Added screenshots for UI changes when relevant
• Included notes for anything not fully tested

Notes:

• Verified both README.md and README-KR.md render cleanly after the update.
• No runtime code changes were included.

Review Notes

Please focus review on:

• whether the reduced badge set feels balanced for the public repo
• whether the Releases link placement in the Live Demo section is more natural than the previous top-of-file placement
• whether the English and Korean README updates stay consistent