Hi @Zoey Liang,
Thank you for posting in this community.
For the wiki page in sharepoint server, there is indeed no publish button, this is by design.
To determine if issue is related to a site itself, please create a new Wiki library in another site and test the search result. And see if the solution in this thread works for you:https://answers.microsoft.com/en-us/msoffice/forum/all/sharepoint-wiki-search-options/802ddbae-7515-479d-8903-42a56ae475b8
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