Remove deprecated code 2024-07 (#21651)

BUILD.bazel

@@ -81,15 +81,13 @@ filegroup(
     visibility = ["//tools:__pkg__"],
 )
 
-# To create a manifest of all installed files for use by drake_bazel_installed,
-# we declare an install target that contains almost everything -- but it can't
-# contain the bazel logic that is generated based on the manifest, so we'll add
-# that in below in the final :install target.
+_INSTALL_TEST_COMMANDS = "install_test_commands"
+
 install(
-    name = "all_install_targets_except_bazel",
+    name = "install",
+    install_tests_script = _INSTALL_TEST_COMMANDS,
     data = ["package.xml"],
     docs = ["LICENSE.TXT"],
-    visibility = ["//tools/install/bazel:__pkg__"],
     deps = [
         "//bindings/pydrake:install",
         "//common:install",
@@ -104,17 +102,6 @@ install(
     ],
 )
 
-_INSTALL_TEST_COMMANDS = "install_test_commands"
-
-install(
-    name = "install",
-    install_tests_script = _INSTALL_TEST_COMMANDS,
-    deps = [
-        ":all_install_targets_except_bazel",
-        "//tools/install/bazel:install",
-    ],
-)
-
 install_test(
     name = "install_test",
     args = ["--install_tests_filename=$(location :{})".format(