Add live progress updates to deepsearch page during indexing/synthesizing

Summary

The deepsearch page does not provide clear, live progress updates to users while indexing or synthesizing. The lack of feedback makes the process appear to hang, causing users to exit the page. The page must show detailed, animated progress from start to end, and the engine itself should be reviewed against best practices for deepsearch engines with custom embeddings and answer synthesis.

Steps to Reproduce

1. Navigate to the deepsearch page.
2. Initiate a search that triggers indexing or synthesizing.
3. Observe the page during the process.

Expected Behaviour

The page should display continuous, detailed, and highly animated progress updates throughout the entire indexing and synthesizing process, clearly communicating each stage to the user.

Actual Behaviour

The page shows little to no progress indication, often appearing to hang, which leads users to exit prematurely.

Environment

Not provided.

Reported by retoor via DevPlace.