Update notice behaviour

[fditrapani]

When you're experimenting with styles on a Free plan, the upgrade notice behaviour feels broken. After you dismiss the notification, it appears again, and again, after every save.

Steps to reproduce

1. Create a free site
2. Apply custom styles
3. Dismiss the banner
4. Make some changes
5. Press save

Recording

https://github.com/user-attachments/assets/99cff22a-e231-4fa1-b18b-ea816df2fd6c

@Copons let's discuss some options to improve this in the comments.

cc @richtabor

[github-actions[bot]]

OpenAI suggested the following labels for this issue:

• [Feature Group] Plans & Upgrades: The issue pertains to the behavior of upgrade notices, which is directly related to the plans and subscription model offered.
• [Feature] Notifications: The problem described involves the notifications about upgrading the plan, highlighting issues with how they are displayed to users.
• [Feature] User Interaction & Engagement: The dissatisfaction with the repeated notifications affects the overall user experience and engagement with the platform.
• [Feature] Site Settings: The behavior of the upgrade notices can be considered part of broader site settings that affect user configuration and preferences.

[fditrapani]

Here are some proposals for how to handle this:

1. Dismiss once per session: We should let you to dismiss it for your current work session. Then show it again if you refresh or close the window, or navigate out of the editor, and come back again.
2. Remove the dismiss button so that the banner always shows.

Ian also mentioned we had a better design for this. I'll track it down and share it for feasability.

[fditrapani]

Closing this in favour of https://github.com/Automattic/dotcom-forge/issues/9890