docs: Standardize language, wording, and API links across all pages

[vdusek]

Summary

• Standardize opening paragraphs to follow "what it is + why it matters" pattern
• Unify example intro phrasing to "The following example shows how to..."
• Migrate all API reference links from raw markdown to <ApiLink> component
• Trim verbose "benefits" paragraphs in pagination and streaming pages
• Add :::tip admonitions to convenience methods and pagination pages

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.77%. Comparing base (2f67a5d) to head (aaed9cd).
⚠️ Report is 2 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #697      +/-   ##
==========================================
- Coverage   94.79%   94.77%   -0.03%     
==========================================
  Files          45       45              
  Lines        4403     4403              
==========================================
- Hits         4174     4173       -1     
- Misses        229      230       +1     

Flag	Coverage Δ
integration	94.77% <ø> (-0.03%)	⬇️

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