docs: fix factual errors in fully-async example page

[Shi-Dong]

Summary

Fixes factual errors in docs/examples/fully-async.md found during a fact-check of every page under docs/examples/ against the actual code in examples/fully_async/.

• Quick-start log output: the page showed a fabricated [trainer] iter 1/3000 ... log block. Replaced with the real stdout prints from fully_async_rollout.py (Creating new global async worker..., Starting async rollout generation for N groups, Rollout completed in ...s! Global worker queue size: N).
• Worker constructor: the doc passed a nonexistent concurrency=args.sglang_server_concurrency kwarg; AsyncRolloutWorker.__init__ only takes (args, data_buffer).
• Worker loop: the doc showed an invented _producer coroutine. Replaced with a condensed version of the real continuous_worker_loop (reap finished tasks, top up in-flight groups via generate_and_rm_group, done-callback onto the output queue), including the real in-flight cap: --rollout-batch-size groups, or --async-max-concurrent-samples ÷ n_samples_per_prompt when set.
• Entry function: the doc showed a made-up async signature. The real generate_rollout_fully_async(args, rollout_id, data_buffer, evaluation=False) is synchronous, rejects evaluation mode, drains --rollout-batch-size groups, recycles aborted groups, and sorts by prompt index.
• What to watch: the doc listed fabricated async/* wandb metrics that the example never logs. Replaced with the real stdout signals plus the standard perf/rollout_time vs perf/actor_train_time comparison.
• MoE variation: the doc claimed tp=4 ep=8, a nonexistent --sglang-enable-ep-moe flag, and a batch-size recommendation not in the script. run_qwen3_30b_a3b_fully_async.py actually uses TP 8 / EP 8, one 8-GPU SGLang engine, --use-tis, and demonstrates the --pause-generation-mode × --update-weight-transfer-mode combinations — every pairing except in_place + p2p, which the script rejects.
• Partial rollout: the doc claimed unfinished trajectories are "saved to disk and resumed". In reality this example recycles aborted groups to the in-memory data buffer but calls reset_for_retry() first, so they regenerate from the prompt; true resume-from-partial is the stock --partial-rollout behavior of the built-in rollout function, which this custom drain loop bypasses. The section now states exactly that.

Test plan

• Verified all replacement snippets against examples/fully_async/fully_async_rollout.py and run_qwen3_30b_a3b_fully_async.py on current main
• Docs render check

[gemini-code-assist]

Caution

The consumer version of Gemini Code Assist on GitHub has been sunset. All code review activity has officially ceased.

[Zhichenzzz]

LGTM! Lets wait till #1717 and #1740 are merged