does APPLE care cover international support in case of hardware trouble.

The easiest way to find out is to contact Apple in your country and ask them since we are all other users and cannot speak for Apple.

Note: Even the Canadian version of the legal terms for Applecare linked include this:

Exclusions apply as described below.

4. What is not Covered?

4.1 Hardware Service and ADH Service

Apple may restrict Hardware Service and ADH Service to the country where the Covered Equipment

was originally purchased.

from here:

https://www.apple.com/legal/sales-support/applecare/applecareplus/2209/220907_applecareplusmac_caen_tc.pdf

As well, that is Applecare for Mac, not a watch.

The easiest way to find out is to contact Apple in your country and ask them since we are all other users and cannot speak for Apple.

Note: Even the Canadian version of the legal terms for Applecare linked include this:

Exclusions apply as described below.

4. What is not Covered?

4.1 Hardware Service and ADH Service

Apple may restrict Hardware Service and ADH Service to the country where the Covered Equipment

was originally purchased.

from here:

https://www.apple.com/legal/sales-support/applecare/applecareplus/2209/220907_applecareplusmac_caen_tc.pdf

As well, that is Applecare for Mac, not a watch. FWIW, the regular mfr's 1 year warranty does have international coverage; the Applecare may or may not. Again, this is for a Mac, not a watch. The Applecare for watch contain the same terms:

Legal - AppleCare+ - Apple

That depends on the product and level of AppleCare. AppleCare+ on a Mac can be used internationally. AppleCare Products - Mac - Apple (CA) for Mac provides global,authorized technicians around the world. iPhone service is only available in the region of purchase.