Database error and error during reinstallation of database

We have updated the WP Statistics Plugin to the latest version (13.0.5) and since then we are getting a database error (sry, for the partially german error code):

WordPress-Datenbank-Fehler: [Unknown column 'page_id' in 'field list']
SELECT <code>page_id</code> FROM <code>wp_statistics_pages</code> WHERE <code>date</code> = '2021-02-08' AND <code>type</code> = 'home' AND <code>id</code> = 779.

This does only happen when a not logged in user visits the site which might be standard behaviour – to be quite honest I am not that firm with your plugin ??

Futhermore if we rerun the database reinstallation routine (found under …/wp-admin/admin.php?page=wps_optimization_page) which we hoped might solve the issue we get the following errors:

WordPress-Datenbank-Fehler: [Duplicate entry '2015-05-01' for key 'unique_date']
ALTER TABLE wp_statistics_visit ADD UNIQUE KEY <code>unique_date</code> (<code>last_counter</code>)

WordPress-Datenbank-Fehler: [Specified key was too long; max key length is 1000 bytes]
ALTER TABLE wp_statistics_visitor CHANGE COLUMN <code>platform</code> platform varchar(180)

WordPress-Datenbank-Fehler: [Specified key was too long; max key length is 1000 bytes]
ALTER TABLE wp_statistics_visitor CHANGE COLUMN <code>version</code> version varchar(180)

WordPress-Datenbank-Fehler: [Duplicate entry '2014-07-10-/unternehmen-verzichten-auf-abschreckungswirkung-in-h' for key 'date_2']
ALTER TABLE wp_statistics_pages CHANGE COLUMN <code>uri</code> uri varchar(190) NOT NULL

WordPress-Datenbank-Fehler: [Incorrect table definition; there can be only one auto column and it must be defined as a key]
ALTER TABLE wp_statistics_pages ADD COLUMN page_id BIGINT(20) NOT NULL AUTO_INCREMENT

WordPress-Datenbank-Fehler: [Key column 'page_id' doesn't exist in table]
ALTER TABLE wp_statistics_pages ADD PRIMARY KEY (<code>page_id</code>)

And lastly when we deactive and reactive your plugin, the activation is successful, but it produces unexpected output, so that there might be something wrong as well.

Any hint what might be wrong here and/or how to deal with this issue would be very much appreciated.

Many thanks