In Xcode 13.4 it doesn't seems to populate PackageFrameworks.
I ended up doing this based on @defagos' post above, but with referencing the nested framework directly:
# Build phase: Copy signing identity
echo "${EXPANDED_CODE_SIGN_IDENTITY}" > /tmp/target-name-signing-identity
# Build post-action: Re-sign nested framework
FRAMEWORK_PATH="$BUILT_PRODUCTS_DIR/$FRAMEWORKS_FOLDER_PATH/Module.framework/Frameworks/Nested.framework/Nested"
CODE_SIGN_IDENTITY=`cat /tmp/target-name-signing-identity`
codesign --sign "$CODE_SIGN_IDENTITY" -f "$FRAMEWORK_PATH"