feat: rename product and runtime to Piik

Rename the active product, Go module, binaries, configuration, protocols and documentation to Piik while retaining the TV mascot and existing media/room behavior.

Use one current private contract without old-name aliases. Preserve SQLite authority and copy compatible local settings once; other settings start fresh. Git-message cleanup and the infrastructure name cutover are coordinated with this phase, with original history and deployment data archived externally.

Validated locally with Web and Go checks, Windows capture compilation, matched Client/Server builds, packaged Client control handshake and history-rewrite integrity checks. Skip duplicate hosted CI for this owner-authorized local release.

[skip ci]

.github/workflows/repository-hygiene.yml

@@ -7,7 +7,7 @@ on:
   workflow_dispatch:
     inputs:
       client_checks:
-        description: Run the optional Screener Client checks
+        description: Run the optional Piik Client checks
         required: false
         default: false
         type: boolean
@@ -31,7 +31,7 @@ jobs:
       - name: Validate tracked project state
         run: sh scripts/check-project-state.sh
         env:
-          SCREENER_BASE_SHA: ${{ github.event.pull_request.base.sha || github.event.before }}
+          PIIK_BASE_SHA: ${{ github.event.pull_request.base.sha || github.event.before }}
       - name: Install dependencies
         run: npm ci
       # The Go build embeds internal/server/webassets/dist, so Vite runs first.
@@ -83,7 +83,7 @@ jobs:
       - name: Upload application release
         uses: actions/upload-artifact@v7
         with:
-          name: screener-app-${{ github.sha }}
+          name: piik-app-${{ github.sha }}
           path: ${{ runner.temp }}/app-release/*
           if-no-files-found: error
           retention-days: 14
@@ -142,7 +142,7 @@ jobs:
       - name: Download application release
         uses: actions/download-artifact@v8
         with:
-          name: screener-app-${{ github.sha }}
+          name: piik-app-${{ github.sha }}
           path: ${{ runner.temp }}/app-release
       - name: Build and verify Client candidate
         run: >-
@@ -153,7 +153,7 @@ jobs:
       - name: Upload Client release candidate
         uses: actions/upload-artifact@v7
         with:
-          name: screener-client-${{ matrix.target }}-${{ github.sha }}
+          name: piik-client-${{ matrix.target }}-${{ github.sha }}
           path: ${{ runner.temp }}/client-release/*
           if-no-files-found: error
           compression-level: 0