SQLWATCH can be removed in two ways

Automated removal with dbatools

dbatools comes with a removal command Uninstall-DbaSqlWatch which removes SQLWATCH objects including database and Agent Jobs.

The Uninstall-DbaSqlWatch will only work if the database was installed using Install-DbaSqlWatch

There are safety measures built into the removal process to make sure that only objects deployed by Install-DbaSqlWatch are removed, including database. If the deployment was into an existing database this will not be removed, analogically, if user tables were added to the SQLWATCH database post-deployment they were not registered as part of the application and thus they will not be removed and subsequently the database will not be dropped.

Manual removal with T-SQL

If SQLWATCH was installed manually the only way to remove is to manually invoke DROP DATABASE and manually remove SQL Agent job.