The Composer commands for upgrade are:

php bin/magento module:disable Tagalys_Sync Tagalys_Analytics Tagalys_Search Tagalys_Mpages Tagalys_Categories Tagalys_Mystore

composer remove tagalys/tagalys-search-magento2

composer require tagalys/tagalys-search-magento2

php bin/magento module:enable Tagalys_Sync Tagalys_Analytics Tagalys_Search Tagalys_Mpages Tagalys_Categories Tagalys_Mystore

php bin/magento setup:upgrade


If required:

php bin/magento setup:di:compile

php bin/magento setup:static-content:deploy