Bug(no code experiment): After saving transformation, toolbar does not update inner html when toggling

Bug Description

Notice that after saving, the title no longer updates when i switch to the control variant. Only after i refresh then it starts to work.

https://github.com/user-attachments/assets/797abaae-fbf3-43e8-b004-922e0e7963ad

How to reproduce

1. Open the toolbar (ensure that no code experiment is enabled, more info here)
2. Create a new experiment through the toolbar
3. Transform one of the html element's inner html for the non control variant
4. Click save as draft
5. Toggle to control variant, you should see that the inner html doesn't switch back to control's despite being currently applied

Additional context

Tested this on my localhost:3000

Debug info

- [ ] PostHog Cloud, Debug information: [please copy/paste from https://us.posthog.com/settings/project-details#variables or https://eu.posthog.com/settings/project-details#variables]
- [ ] PostHog Hobby self-hosted with `docker compose`, version/commit: [please provide]
- [ ] PostHog self-hosted with Kubernetes (deprecated, see [`Sunsetting Kubernetes support`](https://posthog.com/blog/sunsetting-helm-support-posthog)), version/commit: [please provide]

No source file or test is named. Start by reproducing the toolbar flow for a saved no-code web experiment and compare the element's inner HTML while toggling between the control and non-control variants. Done means toggling immediately restores each variant's saved HTML without requiring a refresh.