Refine homepage research and engineering introduction

[p13i]

Summary

• replace the stale student-status homepage copy with a current, organization-neutral introduction grounded in existing résumé and application materials
• add Engineering to the primary navigation and prioritize existing research and engineering posts on the homepage
• improve the homepage heading, headshot alternative text, and small-screen stacking
• update the site subtitle to match the current introduction

Impact

The homepage now gives visitors a concise path into Pramod's research, engineering work, writing, and CV without mentioning or visibly targeting a specific application.

Validation

• npx -y prettier --check --print-width 60 --trailing-comma=none --prose-wrap always index.md _layouts/index.md _data/navbar.yml _config.yml — passed
• git diff --check — passed
• full make lint — completed after providing its missing Python dependencies; it also produced four unrelated baseline-generated diffs, which were restored and are not part of this PR
• user-scoped Jekyll 4 fallback build with the repository plugins preloaded — passed and generated the full site
• local HTTP checks for /, /research/, /engineering/, /writing/, /cv/, and /posts/2023/08/cc-simulations/ — all returned 200
• desktop render inspected at 1440×1100
• mobile emulation at 390×844 — no horizontal overflow (scrollWidth: 390)

Not tested

The repository's prescribed Ruby 2.4 Docker build could not run because the Docker daemon repeatedly timed out resolving registry-1.docker.io while fetching ruby:2.4; the local Jekyll fallback covered full-site generation instead.

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Written by Codex

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