fix: resolve SPA fallback issues (HTML shadowing and MIME type errors)

[barissalihbabacan]

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Description

This PR fixes the SPA dev-server issues that caused the revert of #2173.

Key changes:

1. Fixes HTML shadowing: Skips dist/ lookup for / and /index.html in dev mode to ensure src/html/index.html is loaded correctly instead of stale production builds.
2. Resolves MIME type errors: Restricts the SPA fallback to only navigation requests (HTML/no extension). This ensures that missing assets (.js, .css, .png, etc.) correctly return a 404 instead of an HTML body.
3. Dispatcher Improvements: Refactored startStream to be Promise-based for more reliable connection lifecycle management and added error handling for session creation failures.

What type of PR is this? (check all applicable)

• 🍕 Feature
• 🐛 Bug Fix
• 📝 Documentation Update
• 🎨 Style
• 🧑💻 Code Refactor
• 🔥 Performance Improvements
• ✅ Test
• 🤖 Build
• 🔁 CI

Related Tickets & Documents

Fixes the regression that led to the revert of #2173.

Mobile & Desktop Screenshots/Recordings

(Logic change in dev-server plugin - no visual changes)

Added tests?

• 👍 yes
• 🙅 no, because they aren't needed
• 🙋 no, because I need help

Added to documentation?

• 📜 README.md
• 📓 tech-docs
• 🙅 no documentation needed

[optional] Are there any post-deployment tasks we need to perform?

None.