Hi
Apple Watch Series 3 (GPS + Cellular) is not locked to any specific carrier and has a built-in eSIM that copies information from the iPhone's SIM card.
The built-in cellular features require a carrier plan for your iPhone in your country of use that specifically includes support for Apple Watch Series 3 (GPS + Cellular), including the carrier activating the device on the plan.
If buying Apple Watch Series 3 (GPS + Cellular) in another country, then, in order to use the built-in cellular feature, you would need to buy a model that supports the relevant LTE and UMTS bands for your intended country of use and your supported carrier there.
There are three different regional versions of Apple Watch Series 3 (GPS + Cellular), each supporting different LTE and UMTS bands, as detailed here - there are different models for the US and Germany:
Apple Watch - Carriers - Apple
I suggest that you consult your carrier for further assistance.
If a model is confirmed by your carrier as being compatible, then it may help to check that you are following the instructions here, under the heading "Changing carriers":
Set up and use cellular on Apple Watch Series 3 (GPS + Cellular) - Apple Support
Apple Watch Series 3 (GPS + Cellular) can instead be used without activating the built-in cellular feature, in which case it functions like a GPS-only model, in conjunction with an iPhone 6 or newer model of iPhone (running the latest version of iOS) and a service plan from any carrier.
The built-in cellular features cannot be used when roaming. The warranty terms for an Apple Watch purchased in the US are detailed here:
Apple One (1) Year Limited Warranty
Depending on your carrier's advice, if you need further assistance, I suggest that you contact Apple Support, make a Genius Bar reservation or visit an Apple Authorised Service Provider:
Apple Watch Zentrale für Servicefragen – Apple Support
