Call to undefined method addCacheableDependency() when managing webform with custom assets

Problem/Motivation

(Maybe a regression of #3238391: Webform css/js assets are stale?)

After updating webform (6.0.5 => 6.1.0), I'm getting a PHP error in dblog any time I...

• View a webform with custom CSS.
• Load any build/config pages for managing that webform.

...while logged in with permission to manage webforms.

When I view the webform (while logged-in as this user), the custom CSS is not loaded. (When I view the webform not logged-in as a user with permission to manage webforms, the custom CSS loads fine, and there are no errors in dblog.)

Log entry details:

Type: PHP
Location: https://mysite.com/webform/javascript/my_form?r211ng
Severity: Error

Message:
Error: Call to undefined method Drupal\webform\Routing\WebformUncacheableResponse::addCacheableDependency() in Drupal\webform\Controller\WebformEntityController->css() (line 99 of /code/web/modules/contrib/webform/src/Controller/WebformEntityController.php)
[...backtrace -- lmk if you want it!]

When I remove the custom CSS (via /admin/structure/webform/manage/my_form/settings/assets), the error goes away, but it comes back when I add the custom CSS back.

I have another webform that doesn't have any custom CSS -- I added some fake/placeholder CSS to that form, and when I saved, I got the addCacheableDependency() undefined method error.

When I add custom JavaScript to either of my webforms, there's a second PHP error in dblog:

Error: Call to undefined method Drupal\webform\Routing\WebformUncacheableResponse::addCacheableDependency() in Drupal\webform\Controller\WebformEntityController->javascript() (line 123 of /code/web/modules/contrib/webform/src/Controller/WebformEntityController.php)

(I'm still on core 8.9.19, FWIW.)

Steps to reproduce

(see above)

Proposed resolution

Remaining tasks

User interface changes

API changes

Data model changes