Refactor ADK Web to match IQAI-Agents standards

[Softdev1]

Description

Refactor ADK Web codebase to follow IQAI-Agents architectural patterns, code style, and project structure conventions.

Definition of Done:

• Code structure matches IQAI-Agents architecture
• Linting passes with IQAI-Agents ESLint/Prettier config
• All existing functionality preserved (no regressions)
• Component patterns align with IQAI-Agents conventions

[MarvelNwachukwu]

Think this issue will be resolved with multiple smaller PRs.

[MarvelNwachukwu]

#531

This one improves session management and fixes issue with double toast and errors with switching session