Whenever the email of the partner community user profile is changed the email remain unverfied and no verfiy link would be present beside the email.
The partner user needs to reset the password from the Forgot password link on the community to get the user email verified.
Note: When the System Admin clicks on reset password from the user page, the user password would be reset but not verified.
If you are looking for a way to automate this process ,you can go with Async email template.
https://help.salesforce.com/s/articleView?id=sales.emailadmin_async_email_verification.htm&type=5
https://help.salesforce.com/s/articleView?id=sales.emailadmin_async_email_verification.htm&type=5
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