Populate timeout parameters from REST requests

[nicktindall]

To fix #108224, pull request #108593 brought the documentation into alignment with the current implementation.

When investigating inconsistencies, some opportunities to pass through timeout or master_timeout parameters were identified.

Specifically

• Delete shutdown API (RestDeleteShutdownNodeAction): could populate timeout from REST request
• Get shutdown API (RestGetShutdownStatusAction): could populate master_timeout from REST request
• Put shutdown API (RestPutShutdownNodeAction): could populate timeout from REST request
• Field usage stats API (RestFieldUsageStatsAction): could populate timeout from REST request
• Remove policy from index API (RestRemoveIndexLifecyclePolicyAction): could populate timeout from REST request
• Start watcher service API (RestWatchServiceAction): could populate master_timeout from REST request
• Delete forecasts API (RestDeleteForecastAction): could populate master_timeout from REST request

See https://docs.google.com/spreadsheets/d/1vsBAt5Z8qAidfW9CcDKtfxXfHv4HBWVicJMwvnkhRfc/edit#gid=0 for full findings

Possible duplicate of/overlap with https://github.com/elastic/elasticsearch/issues/107984

[elasticsearchmachine]

Pinging @elastic/es-distributed (Team:Distributed)

[ywangd]

Related, the following APIs only read cluster state and therefore do not need ackTimeout (parsed from the timeout REST parameter). Currently, they basically silently ignore the timeout. However, removing them can be a breaking change. So I am not suggesting to do so. Mostly writing them down here for future references.

• GetLifecyclePolicy API
• GetIndexLifecycleManagementStatus API
• GetMachineLearningMemoryStats API
• GetSnapshotLifecycleManagementStatus API