fix(desktop): Improve Desktop Sidebar Flow when navigating from project to Home page

[OpeOginni]

Issue for this PR

Closes #21885

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

Using GPT-5.4, fixes Desktop sidebar flows, preventing it from showing up with the button when navigating to the home page, and made this work for large screen and mobile screeb

How did you verify your code works?

Tested with a dev run of the electron desktop app and also the app on the browser.

Screenshots / recordings

BEFORE

Screen.Recording.2026-04-10.at.15.50.08.mov

AFTER

Screen.Recording.2026-04-10.at.16.24.25.mov

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

[github-actions]

Hey! Your PR title Improve Desktop Sidebar Flow when navigating from project to Home page doesn't follow conventional commit format.

Please update it to start with one of:

• feat: or feat(scope): new feature
• fix: or fix(scope): bug fix
• docs: or docs(scope): documentation changes
• chore: or chore(scope): maintenance tasks
• refactor: or refactor(scope): code refactoring
• test: or test(scope): adding or updating tests

Where scope is the package name (e.g., app, desktop, opencode).

See CONTRIBUTING.md for details.