ci: Refactor timelord action to use git-warp-time fallback

Updates the timelord action to fall back to git-warp-time when the cache
is completely empty, enabling timestamp restoration even on fresh builds.
When git-warp-time is used, performs an unshallow fetch to get full history,
while subsequent runs use normal fetches. Simplifies the interface by making
inputs optional with sensible defaults.

Adds binary caching for timelord-cli and git-warp-time tools to avoid
repeated installations, and updates paths to use /usr/share/rust/.cargo/bin/
for the catthehacker runner image used by the dind profile (may need updating
if/when switching to standard image).

The main timelord restore now happens inside the Dockerfile itself, as Docker
intentionally wipes all file mtimes on COPY/ADD operations.

docker/Dockerfile

@@ -60,6 +60,7 @@ RUN <<EOF
     curl --retry 5 -L --proto '=https' --tlsv1.2 -sSf https://raw.githubusercontent.com/cargo-bins/cargo-binstall/main/install-from-binstall-release.sh | bash
     cargo binstall --no-confirm cargo-sbom --version $CARGO_SBOM_VERSION
     cargo binstall --no-confirm lddtree --version $LDDTREE_VERSION
+    cargo binstall --no-confirm timelord-cli@3.0.1
 EOF
 
 # Set up xx (cross-compilation scripts)
@@ -81,8 +82,9 @@ RUN rustc --version \
     && xx-cargo --setup-target-triple
 
 # Build binary
-# We disable incremental compilation to save disk space, as it only produces a minimal speedup for this case.
-RUN echo "CARGO_INCREMENTAL=0" >> /etc/environment
+# Configure incremental compilation based on build context
+ARG CARGO_INCREMENTAL=0
+RUN echo "CARGO_INCREMENTAL=${CARGO_INCREMENTAL}" >> /etc/environment
 
 # Configure pkg-config
 RUN <<EOF
@@ -133,6 +135,14 @@ FROM toolchain AS builder
 # Get source
 COPY . .
 
+# Restore timestamps from timelord cache if available
+RUN if [ -f /app/timelord/timelord.db ]; then \
+        echo "Restoring timestamps from timelord cache"; \
+        timelord sync --source-dir /app --cache-dir /app/timelord; \
+    else \
+        echo "No timelord cache found, timestamps will be build time"; \
+    fi
+
 ARG TARGETPLATFORM
 
 # Verify environment configuration