### What problem does this PR solve?
Fixes#14051.
The chat UI already sends an `internet` flag with each request, but the
backend previously triggered Tavily web retrieval whenever
`prompt_config.tavily_api_key` was configured. As a result, web search
could still run even when the internet toggle was off.
This PR makes web search an explicit opt-in at request time:
- `tavily_api_key` only indicates that web search is available
- Tavily retrieval runs only when `internet` is explicitly enabled
- the same behavior now applies to both the normal retrieval path and
the deep-research / reasoning path
This also fixes the no-KB fallback case so chats without KBs fall back
to normal solo chat when `internet` is off.
### Type of change
- [x] Bug Fix (non-breaking change which fixes an issue)
