Standardizing system_prompt usage across the repo

[jamesbraza]

This PR fixes a bunch of minor issues with our prompts, removing thought burden:

• Standardizes use of system prompt setting across the repo
• Standardizes JSON-mode and non-JSON-mode Context generation prompts
• Removes extra whitespace from text summarization prompt

This PR also updates the settings cheatsheet, to make it easier to understand our prompts.

Edit: this is a breaking change w.r.t. user configs, so be warned ⚠️ 🤓

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Pull Request Overview

This PR standardizes prompt handling across the repository by consolidating system_prompt usage and improving the structure of JSON-mode and non-JSON-mode context generation prompts.

• Standardizes use of system prompt setting across the repo
• Refactors JSON-mode and non-JSON-mode Context generation prompts to use consistent structure
• Removes extra whitespace from text summarization prompt and updates settings documentation

Reviewed Changes

Copilot reviewed 10 out of 13 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
src/paperqa/settings.py	Updates prompt field types to support both string and list formats, consolidates JSON prompt structure
src/paperqa/prompts.py	Removes summary_json_prompt, adds include_text_prompt_template for consistent formatting
src/paperqa/core.py	Refactors message handling to support multiple user prompts with proper system message placement
src/paperqa/docs.py	Simplifies prompt template handling logic
tests/test_paperqa.py	Updates test to work with new list-based prompt structure
src/paperqa/configs/*.json	Updates configuration files to use new list-based JSON prompt format
docs/tutorials/*	Updates documentation to reflect new prompt structure
README.md	Updates settings cheatsheet with improved descriptions

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[whitead]

I think this is good, but we'll have to merge in v6 since it's breaking change.