The reset password URL generally wouldn’t show up in Omeka’s error log: in fact Omeka probably doesn’t even see that there’s an error. If your server’s simply not set up to successfully deliver mail, the messages are likely floating around in whatever queue or spool the server’s set up with by default. Nothing has changed about this process with PHP 7; PHP’s standard email support has always relied on the server’s MTA to actually send the mail. If you know what MTA you have, you can probably find the message in its queue, log, or area for failed messages.
It is possible to set a password manually in the database, but if you’re in there it’s probably simpler to just go and look at the users_activations table to get the reset link. Each row has a “url” column, and the reset password link is formed by appending that “url” value to the end of the URL admin/users/activate/u/