Refactor TransportIndicesAliasesAction action loop for ease of understanding

[parkertimmins]

Description

While working on #106514 , it became clear that the main method of TransportIndicesAliasesAction has grown unwieldy. In particular, the large loop over request actions with multiple continue statements is difficult to understand.

A possible refactoring would involve moving the sections of the loop that focus on concrete indices and data streams into their own functions. Then rather than continuing from the data streams portion of the loop (here), the data stream function would call into the concrete index function.

[elasticsearchmachine]

Pinging @elastic/es-data-management (Team:Data Management)