README revamp: fix broken commands, add demo GIF, correct competitor table, polished

[agentecobuilder]

Summary

README revamp to fix several broken user flows, improve clarity, and tighten product positioning. All commands and code blocks were tested locally on a fresh macOS environment to confirm they work.

Substantive fixes (issues that would affect users)

• Quick Start now uses commands that actually ship. Removed references to stratix init, which doesn't exist in the SDK, and replaced it with the working PublicClient flow.
• Fixed the broken "Next Steps" section, which had the same non-existent stratix init command. Replaced it with the actual working install, API key, and first-call sequence.
• Quoted "layerlens[cli]" in install commands. It was failing in zsh (default macOS shell) because of the unquoted brackets.
• Switched python to python3. Default macOS no longer ships a python alias, so the original command was failing.
• Clarified the two-client model. Added a callout explaining when to use PublicClient vs Stratix, so users aren't confused when pc appears in code before it's introduced.
• Promoted the early-access install warning. The note about needing --extra-index-url is now a GitHub callout instead of a line that's easy to skim past.
• Removed the broken CI badge that was rendering as a broken image icon.

Competitor table updates

• DeepEval: "~14 metrics" → "50+ metrics" (per their official live site)
• Langfuse prompt-level comparison: "Not built-in" → "Prompt experiments + side-by-side (UI)"

Additions

• Demo GIF at the top of the README, showing the SDK in action, listing 217 frontier models from 4 different vendors in 5 lines of Python.
• Pricing section between the comparison table and Installation, clarifying the free vs. Stratix Premium split.
• Replaced a dead link embed with the richer samples/ directory.
• Replaced previous Examples table with more rich Samples table