I honestly have no idea at this point what could be wrong exactly. I recall someone had a very similar issue years ago, when using a multisite installation, but it was resolved and the plugin was updated accordingly, and never heard of that issue again.
It was basically something with the database prefix. His installation returned incorrect database brefixes for some reason. So variable $wpdb->prefix and $wpdb->base_prefix resulted the same value on each site, where the base_prefix attribute has to be the main database table.
The only thing I can think of is, that the plugin might have been activated from a child site not from the multisite root causing a similar issue, and the database tables might have been created with the incorrect prefix. It should not happen of course, but if the $wpdb->base_prefix returns an incorrect value, then it might do.
Can you please try to deactivate and activate the plugin from the multisite root site?Best,
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