add database.NotFoundError helper type (#63671)

Use it in the 1 place it seemed obvious. I have other changes where it
will be used in more places. This helps standardize our codebase.

## Test plan

CI

internal/database/BUILD.bazel

@@ -28,6 +28,7 @@ go_library(
         "conf.go",
         "database.go",
         "doc.go",
+        "errors.go",
         "event_logs.go",
         "event_logs_scrape_state_own.go",
         "executor_secret_access_logs.go",
@@ -200,6 +201,7 @@ go_test(
         "database_test.go",
         "dbstore_db_test.go",
         "err_test.go",
+        "errors_test.go",
         "event_logs_test.go",
         "executor_secret_access_logs_test.go",
         "executor_secrets_internal_test.go",

internal/database/errors.go

@@ -0,0 +1,19 @@
+package database
+
+// resourceNotFoundError is an error that indicates that a database resource was not found. It can be
+// returned by methods that get a single resource (such as Get or GetByXyz).
+//
+// errcode.IsNotFound(err) == true for notFoundError values.
+type resourceNotFoundError struct {
+	noun string
+}
+
+func (e resourceNotFoundError) Error() string {
+	const notFound = "not found"
+	if e.noun == "" {
+		return notFound
+	}
+	return e.noun + " " + notFound
+}
+
+func (resourceNotFoundError) NotFound() bool { return true }

internal/database/errors_test.go

@@ -0,0 +1,22 @@
+package database
+
+import (
+	"testing"
+
+	"github.com/sourcegraph/sourcegraph/internal/errcode"
+)
+
+func TestResourceNotFoundError(t *testing.T) {
+	err := resourceNotFoundError{"foo"}
+	if want := "foo not found"; err.Error() != want {
+		t.Errorf("got %q, want %q", err, want)
+	}
+
+	if !errcode.IsNotFound(resourceNotFoundError{"foo"}) {
+		t.Fatal()
+	}
+	if !errcode.IsNotFound(&resourceNotFoundError{"foo"}) {
+		t.Fatal()
+	}
+
+}

internal/database/search_contexts.go

@@ -19,7 +19,7 @@ import (
 	"github.com/sourcegraph/sourcegraph/lib/errors"
 )
 
-var ErrSearchContextNotFound = errors.New("search context not found")
+var ErrSearchContextNotFound = resourceNotFoundError{noun: "search context"}
 
 func SearchContextsWith(logger log.Logger, other basestore.ShareableStore) SearchContextsStore {
 	return &searchContextsStore{logger: logger, Store: basestore.NewWithHandle(other.Handle())}