I hear you, though, even in Germany there are other separate police forces under different ministries, like the Zoll (customs and immigration), the Feldjaeger (military police), and Justizvollzug (correctional officers and prisoner transport) - and each one of them has SWAT-like teams in addition to the forces of state and federal police.

There are also a lot of other public officers with limited police powers and different reporting, just like in the US - officers of the courts, public health inspectors, the Ordnungsamt (public order office), forest rangers, officers of the bureau of standards etc.

Until a few decades ago, it was even more splintered, and the border police and railway police were only integrated into the federal police in the 1990s if I am not mistaken...