So it *might* also be a Webform issue, if it doesn't happen in other Multistep forms, I'm not sure. But still unexpected, so I'll keep the status.
I'm facing the same problem with my custom multistep forms.
One observation is that the persistence mechanism and the mentioned option in the captcha module rely on the captcha status stored in the captcha_sessions table. However, it appears that the captcha status is not being updated at all within the ReCaptcha module.
Additionally, I'm unsure whether the ReCaptcha module needs to perform the action mentioned. It might be the responsibility of the captcha module. The captcha status isn't managed if the cacheable attribute during the generation operation is set, which is the case with ReCaptcha.
To me, it makes more sense for the captcha status to be managed entirely by the captcha module.
Adding to the discussion, it appears that the persistence settings were previously overlooked #3363653 🐛 reCAPTCHA ignores “Omit challenges in a multi-step/preview workflow…" setting Needs work and not related to the patch.
I faced the same problem until I realized I was missing the core-dev package. Running composer require --dev drupal/core-dev solved the problem.