Networks and Sites: Display Network Settings errors

[Sukhendu2002]

Trac ticket: https://core.trac.wordpress.org/ticket/18088

Network Settings validation errors were lost during the redirect after form submission. Consequently, invalid values such as an invalid Network Admin Email displayed a “Settings saved” success notice even though the value was rejected.

This PR:

• Stores Network Settings errors in a site transient before redirecting.
• Restores and deletes those errors on the redirected Network Admin request.
• Displays validation errors instead of the success notice.
• Shows the success notice only for updated=true when no errors exist.

The network-option fallback behavior tracked in #35379 remains outside this PR’s scope.

Use of AI Tools

AI assistance: Yes
Tool(s): pi
Model(s): GPT-5.6
Used for: Code review and PR description drafting; final implementation and tests were reviewed and edited by me.

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