fix: correct case statement syntax in TARGETARCH -> RID mapping

The previous inline case statement was missing proper variable assignment.
Use 'case' to set DOTNET_RID directly instead of trying to capture output
of a command substitution that contained a multi-branch case.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/LiveRecorder.WebApi/Dockerfile

@@ -24,7 +24,11 @@ ENV HTTP_PROXY=${HTTP_PROXY} \
 # resolve to the correct platform. Framework-dependent output — apphost stays
 # at /p:UseAppHost=false.
 ARG TARGETARCH
-RUN DOTNET_RID=$(case "$TARGETARCH" in amd64) echo linux-x64 ;; arm64) echo linux-arm64 ;; *) echo "unknown: $TARGETARCH" >&2; exit 1 ;; esac) ; \
+RUN case "$TARGETARCH" in \
+      amd64) DOTNET_RID=linux-x64 ;; \
+      arm64) DOTNET_RID=linux-arm64 ;; \
+      *) echo "ERROR: unknown TARGETARCH=$TARGETARCH" >&2; exit 1 ;; \
+    esac ; \
     echo "Building for TARGETARCH=$TARGETARCH -> RID=$DOTNET_RID"
 
 COPY . .