## Why

Opening the management terminal currently places an operator at the top of the replayed history, so the oldest item in the selected window is visible instead of the newest runtime output. The SSE history limit is also applied independently to every log stream, allowing the initial response size to grow with stream count instead of remaining bounded for the server view.

## What Changes

- Bound SSE history replay by a server-wide recent-entry window, capped at 10,000 entries, rather than replaying the requested limit for each stream.
- Preserve chronological replay order so a browser can render the selected recent window and begin at its newest output.
- Make the management terminal retain at most 10,000 rendered lines, initially follow the bottom, pause auto-follow when an operator scrolls away, and resume it when the operator returns to the bottom.
- Keep `POST /api/v1/log-streams/query` as the bounded, explicit historical cursor API; do not add full-history browser loading.

## Capabilities

### New Capabilities

- `bounded-server-log-view`: Bounded server-wide SSE history replay and management-terminal auto-follow behavior for live server log views.

### Modified Capabilities

- None.

## Impact

- Affects the Platform server log SSE endpoint, its Go tests, and the persisted-log history selection path.
- Affects the platform_web log event client types and management terminal component/tests.
- Does not change Run-to-Platform durable batch ingest, browser authorization, plugin-declared log sources, or game-specific behavior.