diff --git a/.clang-format b/.clang-format
index d1c25d369de3..a66b36f7ef82 100644
--- a/.clang-format
+++ b/.clang-format
@@ -31,7 +31,7 @@ IncludeCategories:
   - Regex:    '^[<"](aio|arpa/inet|assert|complex|cpio|ctype|curses|dirent|dlfcn|errno|fcntl|fenv|float|fmtmsg|fnmatch|ftw|glob|grp|iconv|inttypes|iso646|langinfo|libgen|limits|locale|math|monetary|mqueue|ndbm|netdb|net/if|netinet/in|netinet/tcp|nl_types|poll|pthread|pwd|regex|sched|search|semaphore|setjmp|signal|spawn|stdalign|stdarg|stdatomic|stdbool|stddef|stdint|stdio|stdlib|stdnoreturn|string|strings|stropts|sys/ipc|syslog|sys/mman|sys/msg|sys/resource|sys/select|sys/sem|sys/shm|sys/socket|sys/stat|sys/statvfs|sys/time|sys/times|sys/types|sys/uio|sys/un|sys/utsname|sys/wait|tar|term|termios|tgmath|threads|time|trace|uchar|ulimit|uncntrl|unistd|utime|utmpx|wchar|wctype|wordexp)\.h[">]$'
     Priority: 20
   # C++ system headers (as of C++17).
-  - Regex:    '^[<"](algorithm|any|array|atomic|bitset|cassert|ccomplex|cctype|cerrno|cfenv|cfloat|charconv|chrono|cinttypes|ciso646|climits|clocale|cmath|codecvt|complex|condition_variable|csetjmp|csignal|cstdalign|cstdarg|cstdbool|cstddef|cstdint|cstdio|cstdlib|cstring|ctgmath|ctime|cuchar|cwchar|cwctype|deque|exception|filesystem|forward_list|fstream|functional|future|initializer_list|iomanip|ios|iosfwd|iostream|istream|iterator|limits|list|locale|map|memory|memory_resource|mutex|new|numeric|optional|ostream|queue|random|ratio|regex|scoped_allocator|set|shared_mutex|sstream|stack|stdexcept|streambuf|string|string_view|strstream|system_error|thread|tuple|type_traits|typeindex|typeinfo|unordered_map|unordered_set|utility|valarray|variant|vector)[">]$'
+  - Regex:    '^[<"](algorithm|any|array|atomic|bitset|cassert|ccomplex|cctype|cerrno|cfenv|cfloat|charconv|chrono|cinttypes|ciso646|climits|clocale|cmath|codecvt|complex|condition_variable|csetjmp|csignal|cstdalign|cstdarg|cstdbool|cstddef|cstdint|cstdio|cstdlib|cstring|ctgmath|ctime|cuchar|cwchar|cwctype|deque|exception|execution|filesystem|forward_list|fstream|functional|future|initializer_list|iomanip|ios|iosfwd|iostream|istream|iterator|limits|list|locale|map|memory|memory_resource|mutex|new|numeric|optional|ostream|queue|random|ratio|regex|scoped_allocator|set|shared_mutex|sstream|stack|stdexcept|streambuf|string|string_view|strstream|system_error|thread|tuple|type_traits|typeindex|typeinfo|unordered_map|unordered_set|utility|valarray|variant|vector)[">]$'
     Priority: 30
   # Other libraries' h files (with angles).
   - Regex:    '^<'
diff --git a/bindings/pydrake/.clang-format b/bindings/pydrake/.clang-format
index b9f2926b2c31..59718ff3501a 100644
--- a/bindings/pydrake/.clang-format
+++ b/bindings/pydrake/.clang-format
@@ -50,7 +50,7 @@ IncludeCategories:
   - Regex:    '^[<"](aio|arpa/inet|assert|complex|cpio|ctype|curses|dirent|dlfcn|errno|fcntl|fenv|float|fmtmsg|fnmatch|ftw|glob|grp|iconv|inttypes|iso646|langinfo|libgen|limits|locale|math|monetary|mqueue|ndbm|netdb|net/if|netinet/in|netinet/tcp|nl_types|poll|pthread|pwd|regex|sched|search|semaphore|setjmp|signal|spawn|stdalign|stdarg|stdatomic|stdbool|stddef|stdint|stdio|stdlib|stdnoreturn|string|strings|stropts|sys/ipc|syslog|sys/mman|sys/msg|sys/resource|sys/select|sys/sem|sys/shm|sys/socket|sys/stat|sys/statvfs|sys/time|sys/times|sys/types|sys/uio|sys/un|sys/utsname|sys/wait|tar|term|termios|tgmath|threads|time|trace|uchar|ulimit|uncntrl|unistd|utime|utmpx|wchar|wctype|wordexp)\.h[">]$'
     Priority: 20
   # C++ system headers (as of C++17).
-  - Regex:    '^[<"](algorithm|any|array|atomic|bitset|cassert|ccomplex|cctype|cerrno|cfenv|cfloat|charconv|chrono|cinttypes|ciso646|climits|clocale|cmath|codecvt|complex|condition_variable|csetjmp|csignal|cstdalign|cstdarg|cstdbool|cstddef|cstdint|cstdio|cstdlib|cstring|ctgmath|ctime|cuchar|cwchar|cwctype|deque|exception|filesystem|forward_list|fstream|functional|future|initializer_list|iomanip|ios|iosfwd|iostream|istream|iterator|limits|list|locale|map|memory|memory_resource|mutex|new|numeric|optional|ostream|queue|random|ratio|regex|scoped_allocator|set|shared_mutex|sstream|stack|stdexcept|streambuf|string|string_view|strstream|system_error|thread|tuple|type_traits|typeindex|typeinfo|unordered_map|unordered_set|utility|valarray|variant|vector)[">]$'
+  - Regex:    '^[<"](algorithm|any|array|atomic|bitset|cassert|ccomplex|cctype|cerrno|cfenv|cfloat|charconv|chrono|cinttypes|ciso646|climits|clocale|cmath|codecvt|complex|condition_variable|csetjmp|csignal|cstdalign|cstdarg|cstdbool|cstddef|cstdint|cstdio|cstdlib|cstring|ctgmath|ctime|cuchar|cwchar|cwctype|deque|exception|execution|filesystem|forward_list|fstream|functional|future|initializer_list|iomanip|ios|iosfwd|iostream|istream|iterator|limits|list|locale|map|memory|memory_resource|mutex|new|numeric|optional|ostream|queue|random|ratio|regex|scoped_allocator|set|shared_mutex|sstream|stack|stdexcept|streambuf|string|string_view|strstream|system_error|thread|tuple|type_traits|typeindex|typeinfo|unordered_map|unordered_set|utility|valarray|variant|vector)[">]$'
     Priority: 30
   # Other libraries' h files (with angles).
   - Regex:    '^<'