Who removed the standard Joomla! Templates Protostar and Beez3 during cleanup process, after each update the files are available again.
However, they can not be selected in the backend. The cause is the lack of database entries.
Restore the standard Templates via FTP
If not already done during the update, take a new Joomla! Installation and simply copy the two standard template folders.
The same applies to the backend template.
Insert the database records
In the Joomla! database also the entries must be uploaded again, so that the Templates are selectable in the backend:
INSERT INTO `#__extensions` (`extension_id`, `package_id`, `name`, `type`, `element`, `folder`, `client_id`, `enabled`, `access`, `protected`, `manifest_cache`, `params`, `custom_data`, `system_data`, `checked_out`, `checked_out_time`, `ordering`, `state`) VALUES (503, 0, 'beez3', 'template', 'beez3', '', 0, 1, 1, 0, '{\"name\":\"beez3\",\"type\":\"template\",\"creationDate\":\"25 November 2009\",\"author\":\"Angie Radtke\",\"copyright\":\"Copyright (C) 2005 - 2018 Open Source Matters, Inc. All rights reserved.\",\"authorEmail\":\"\",\"authorUrl\":\"http:\\/\\/www.der-auftritt.de\",\"version\":\"3.1.0\",\"description\":\"TPL_BEEZ3_XML_DESCRIPTION\",\"group\":\"\",\"filename\":\"templateDetails\"}', '{\"wrapperSmall\":\"53\",\"wrapperLarge\":\"72\",\"sitetitle\":\"\",\"sitedescription\":\"\",\"navposition\":\"center\",\"templatecolor\":\"nature\"}', '', '', 0, '0000-00-00 00:00:00', 0, 0), (504, 0, 'hathor', 'template', 'hathor', '', 1, 1, 1, 0, '{\"name\":\"hathor\",\"type\":\"template\",\"creationDate\":\"May 2010\",\"author\":\"Andrea Tarr\",\"copyright\":\"Copyright (C) 2005 - 2018 Open Source Matters, Inc. All rights reserved.\",\"authorEmail\":\"\",\"authorUrl\":\"\",\"version\":\"3.0.0\",\"description\":\"TPL_HATHOR_XML_DESCRIPTION\",\"group\":\"\",\"filename\":\"templateDetails\"}', '{\"showSiteName\":\"0\",\"colourChoice\":\"0\",\"boldText\":\"0\"}', '', '', 0, '0000-00-00 00:00:00', 0, 0), (506, 0, 'protostar', 'template', 'protostar', '', 0, 1, 1, 0, '{\"name\":\"protostar\",\"type\":\"template\",\"creationDate\":\"4\\/30\\/2012\",\"author\":\"Kyle Ledbetter\",\"copyright\":\"Copyright (C) 2005 - 2018 Open Source Matters, Inc. All rights reserved.\",\"authorEmail\":\"\",\"authorUrl\":\"\",\"version\":\"1.0\",\"description\":\"TPL_PROTOSTAR_XML_DESCRIPTION\",\"group\":\"\",\"filename\":\"templateDetails\"}', '{\"templateColor\":\"\",\"logoFile\":\"\",\"googleFont\":\"1\",\"googleFontName\":\"Open+Sans\",\"fluidContainer\":\"0\"}', '', '', 0, '0000-00-00 00:00:00', 0, 0);
INSERT INTO `#__template_styles` (`id`, `template`, `client_id`, `home`, `title`, `params`) VALUES (4, 'beez3', 0, '0', 'Beez3 - Default', '{\"wrapperSmall\":\"53\",\"wrapperLarge\":\"72\",\"logo\":\"images\\/joomla_black.png\",\"sitetitle\":\"Joomla!\",\"sitedescription\":\"Open Source Content Management\",\"navposition\":\"left\",\"templatecolor\":\"personal\",\"html5\":\"0\"}'), (5, 'hathor', 1, '0', 'Hathor - Default', '{\"showSiteName\":\"0\",\"colourChoice\":\"\",\"boldText\":\"0\"}'), (7, 'protostar', 0, '0', 'protostar - Default', '{\"templateColor\":\"\",\"logoFile\":\"\",\"googleFont\":\"1\",\"googleFontName\":\"Open+Sans\",\"fluidContainer\":\"0\"}');
Just replace the "#_" prefixes with your individual table prefix. The IDs should not cause any problems, as these are the original IDs of Joomla!
If so, a blank value '' can be entered instead of the first ID column so that the IDs are determined automatically.