Do I have vacation entitlement at ucm?

Your employment contract with ucm always regulates the holiday entitlement. This reads:

§10 Vacation

The holiday entitlement is based on § 11 MTV BAP in the current version. The holiday allowance of the employee is to be calculated on the basis of § 13.3 MTV BAP. Otherwise, the provisions of the Federal Holidays Act apply.

You can view the BAP framework collective agreement here:

https://www.personaldienstleister.de/fileadmin//user_upload/11_Publikationen/211011_TarifvertragZeitarbeit_Dez2019_Webversion.pdf#211011_TarifvertragZeitarbeit_Dez2019_Webversion.indd%3A.7926%3A210