Polish public NuGet presentation

[Courtland9777]

Summary

• Update README landing copy, badges, install command, and status language for the published 0.1.0-alpha.1 prerelease.
• Align status/readiness/runbook/release-candidate docs with Trusted Publishing completion, NuGet verification, and future-release boundaries.
• Update package release notes and changelog so public metadata no longer says the package is unpublished.

Validation

• git diff --check: passed
• dotnet restore IntervalTree.Net.sln: initial sandbox run failed writing NuGet cache under /home/courtland; rerun with normal cache access passed
• dotnet build IntervalTree.Net.sln --configuration Release --no-restore: passed, 0 warnings, 0 errors
• dotnet test IntervalTree.Net.sln --configuration Release --no-build: passed, 23 tests
• dotnet pack src/IntervalTree.Net/IntervalTree.Net.csproj --configuration Release --no-build --output artifacts/packages: passed, created .nupkg and .snupkg
• bash scripts/smoke-test-local-package.sh: passed
• bash scripts/inspect-package-artifacts.sh artifacts/packages: passed

Boundaries

• No GitHub release or git tag created.
• No NuGet version beyond 0.1.0-alpha.1 approved or created.
• No secrets, API keys, new workflow triggers, or broader release automation added.
• No implementation behavior or public API changes.