Centralize build output and generate OS-specific startup.json

- All DLLs now output to lib\[Configuration]\[TargetFramework]\ at repo root (see Directory.Build.props)
- .gitignore updated to exclude /lib/
- On first run, startup.json is auto-generated with OS-appropriate default paths (Windows, Linux, macOS, or portable)
- Removes null/example config; generated config is immediately usable and clearly documented
- Extensive new documentation: build output, startup.json logic, visual guides, and code proofs
- Publish profile now deletes existing files for clean deploys
- No breaking changes: existing startup.json files are preserved
- Improves first-run UX, deployment, and cross-platform consistency

Directory.Build.props

@@ -5,6 +5,16 @@
     <Nullable>enable</Nullable>
   </PropertyGroup>
 
+  <!-- Centralized output directory configuration -->
+  <PropertyGroup>
+    <!-- Set the base output path to lib folder at repository root -->
+    <BaseOutputPath>$(MSBuildThisFileDirectory)lib\</BaseOutputPath>
+    <!-- Build output goes to lib\[Configuration] (e.g., lib\Debug, lib\Release) -->
+    <OutputPath>$(BaseOutputPath)$(Configuration)\</OutputPath>
+    <!-- Keep intermediate files in traditional obj folder -->
+    <BaseIntermediateOutputPath>obj\</BaseIntermediateOutputPath>
+  </PropertyGroup>
+
   <PropertyGroup>
     <TreatWarningsAsErrors>true</TreatWarningsAsErrors>
     <WarningsNotAsErrors>NU1902;NU1903</WarningsNotAsErrors>