Items added to settings_errors transient are not displayed on settings update

[Mai-Saad]

Before submitting an issue please check that you’ve completed the following steps:

• Made sure you’re on the latest version => 3.9.2
• Used the search feature to ensure that the bug hasn’t been reported before =>yes

Describe the bug
A clear and concise description of what the bug is.
When using an invalid regex, it is removed from UI without displaying a notice

To Reproduce
Steps to reproduce the behavior:

1. Go to Advanced rules
2. Add gtag( in Always Purge URLs
3. Save
4. gtag( removed and no notice is displayed

Expected behavior
A clear and concise description of what you expected to happen.
Notice is displayed

Additional context
Add any other context about the problem here.
As per change here #4195 (comment) , the notice shall be The following pattern has been escaped to prevent errors:

Backlog Grooming (for WP Media dev team use only)

• Reproduce the problem
• Identify the root cause
• Scope a solution
• Estimate the effort

[iCaspar]

This issue is blocking
#4472
#4327
#4013

[iCaspar]

Grooming Notes:

Reproduced: ✔️

Root cause: ✔️
Adding settings_errors to the transient does not persist them across the page load because other calls to the settings API get_settings_errors() deletes the transient before we have a chance in our settings to get the contents.

Solution scope: ✔️
Instead of setting the transient, we can use WP's add_settings_error() to store the errors/notices.

Estimated effort:
[XS]