Improve API reference documentation #637

Summary

The current API reference documentation is pretty messy and needs to be cleaned up. We've already improved the API reference in the SDK and Crawlee — now it's time to do the same for the Client.

Goals

• The API reference should contain only public symbols (no internals)
• It should be well-organized into clear sections:
  • Apify API client
  • HTTP clients
  • Resource clients
  • Models
  • (possibly more — TBD)

Context

This aligns with the documentation improvements already done in:

• Apify SDK - Improve grouping in API docs apify-sdk-python#508
• Crawlee - Improve grouping in API docs crawlee-python#1293