[workspace] Deprecate the petsc external (#19890)

We anticipate no longer using this soon, so it's time to start the
clock for its removal.

multibody/fem/BUILD.bazel

@@ -404,7 +404,7 @@ drake_cc_library(
     ],
     deps = [
         "//common:unused",
-        "@petsc",
+        "@petsc//:petsc_nowarn",
     ],
 )
 

tools/workspace/default.bzl

@@ -245,6 +245,8 @@ def add_default_repositories(excludes = [], mirrors = DEFAULT_MIRRORS):
     if "osqp_internal" not in excludes:
         osqp_internal_repository(name = "osqp_internal", mirrors = mirrors)
     if "petsc" not in excludes:
+        # The @petsc external is deprecated in Drake's WORKSPACE and will be
+        # removed on or after 2023-11-01.
         petsc_repository(name = "petsc", mirrors = mirrors)
     if "picosha2" not in excludes:
         picosha2_repository(name = "picosha2", mirrors = mirrors)

tools/workspace/petsc/package.BUILD.bazel

@@ -147,6 +147,14 @@ cc_library(
         "@drake//tools/workspace/petsc:stubs",
     ],
     visibility = ["//visibility:public"],
+    deprecation = "The @petsc external is deprecated in Drake's WORKSPACE and will be removed on or after 2023-11-01.",  # noqa
+)
+
+# An alias that avoids the deprecation warning (for Drake's internal use only).
+cc_library(
+    name = "petsc_nowarn",
+    deps = [":petsc"],
+    visibility = ["//visibility:public"],
 )
 
 genrule(

tools/workspace/petsc/repository.bzl

@@ -3,6 +3,9 @@ load("@drake//tools/workspace:github.bzl", "github_archive")
 def petsc_repository(
         name,
         mirrors = None):
+    """The @petsc external is deprecated in Drake's WORKSPACE and will be
+    removed on or after 2023-11-01.
+    """
     github_archive(
         name = name,
         repository = "petsc/petsc",