#1783 web: add persistent chats and MCP management

Description

## Summary

Adds a native-feeling persistence and MCP-management layer to Strata's existing Web UI without changing the inference engine or model-specific defaults.

## What changed

- Persist Web UI conversations as JSON under `conversations/`, with a docked conversation list, switching, New Chat creating a new conversation instead of clearing history, and delete confirmation.
- Add a dedicated **MCP** tab between Monitor and About.
- Manage any number of MCP servers using either transport Strata already supports:
  - Streamable HTTP via `url`.
  - stdio via `command`, JSON `args`, optional `cwd`, and JSON `env`.
- Show per-server connection state, transport, and enumerated tools.
- Add exact context usage through Strata's current template/tokenizer path, displayed as a semi-circular used/total gauge.
- Add dependency-free syntax highlighting for fenced code blocks while preserving the existing Markdown renderer and Strata styling.

### MCP configuration safety

The UI is a frontend for Strata's existing MCP backend rather than a parallel protocol implementation.

- HTTP header values and stdio environment values are never returned to the browser.
- Hidden HTTP headers are preserved only while the URL is unchanged.
- Hidden stdio env values are preserved only while command/args/cwd are unchanged; changing the launch identity drops them instead of silently forwarding credentials to a different process.
- Editing/removing one named server leaves the others untouched.
- stdio is explicitly described as starting a local process with the user's rights.
- Changes are persisted to the current run config and take effect after restarting Strata.

### Conversation persistence

- UUID-backed IDs are validated before becoming paths.
- Writes use a unique temporary file followed by atomic replace.
- Conversation files are capped at 64 MiB.
- `/conversations/` is gitignored.
- The existing browser-local chat remains only as a fallback/migration path.

### Context meter

`/context-count` runs the current OpenAI-shaped Web UI history through Strata's own conversion/template/tokenizer path, including MCP tool schemas when enabled. The displayed count is therefore the actual prompt shape Strata will send, not a character estimate.

## Validation

Clean worktree based on current `origin/main`:

- `serve.test_local_ui`: **9/9 passed**
- `serve.test_server`: **271/271 passed**
- `serve.test_mcp`: **25/25 passed**
- `serve.test_runconfig`: **9/9 passed**
- `node --check serve/web/app.js`: passed
- Python compile checks: passed
- `git diff --check`: passed

A live acceptance test also added a stdio server beside an existing HTTP server, verified both were listed together, confirmed secret env values were not returned to the browser, verified the preserve/drop rules across edits, removed only the temporary server, and confirmed the original server remained unchanged.

## Screenshots

![Persistent conversations, syntax highlighting, and context gauge](https://raw.githubusercontent.com/VykosX/Strata/pr-assets/screenshots/PR_CHAT.png)

![Multiple MCP servers using HTTP and stdio](https://raw.githubusercontent.com/VykosX/Strata/pr-assets/screenshots/PR_MCP.png)