Interactive fitting session in the browser (WebSocket-streamed iterates)

[joglekara]

Later phase — the successor to the "Interactive (Under Development)" Streamlit mode. tesseract_ui.py runs an optax loop inside Streamlit reruns against a Tesseract on EC2 (started/stopped via boto3; the ECS tesseract services were removed in continuum-infra #68/#74). The rerun-the-whole-script model is exactly what made this feel clunky; a real frontend does it properly.

Shape

• Backend session endpoint: start a fitting session (initial params + target spectrum), run the optimization loop server-side, stream iterates (params, loss, predicted spectrum) over a WebSocket
• Frontend: live-updating spectrum overlay + parameter/loss traces; pause / resume / nudge-a-parameter / re-seed interactions
• Session lifecycle: timeouts, one-session-per-user limits, cleanup

Open design questions

• Where the forward model runs: in-service CPU (the 1D forward pass may be fast enough on Fargate), a revived Tesseract service, or on-demand Batch — cost/latency call that needs a measurement first
• Real data vs synthetic: the Streamlit version only fit synthetic spectra; wiring a session to a lineout of a real run (from the run detail page, Browser frontend: run detail view (interactive spectrogram, lineouts, profiles, config diff) #32) is the actually-useful version

Depends on #32; infra conversation to be opened once the compute question has a number attached.