feat(settings): add profile form validation, simulated persistence, a…

[Anadudev]

closes #295

Summary of Changes

Profile Validation Layer

• Implemented strongly typed profile field validation in profile.ts.
• Added constraints for username, hex theme colors, avatar URL format, bio length, and social handles (Twitter, Discord, GitHub).

Simulated Profile Persistence

• Created mock backend persistence handlers in api.ts using localStorage to retain profile changes between sessions.
• Added artificial network latency to mirror actual API responsiveness.

useApi Hooks updates

• Adjusted useApi.ts to reset error states and propagate caught errors to form handlers.

Layout Positioning Adjustments

• Adjusted NetworkBadge.tsx to clear the sidebar space on desktop and not overlap title content on mobile.
• Rendered <NetworkBadge /> in teams/page.tsx for layout consistency.

UI Integration

• Connected mount fetching and handleSave action to loading state and error handlers in settings/page.tsx.
• Displayed input validation messages and alert banners.

[MaryammAli]

LGTM