Can I use the apple watch SE edition to make and receive calls if I leave my phone at home?

The Apple Shares the iPhone's phone number, and the carriers that support the Apple Watch charge a monthly fee. In the U.S. the fee is $10 per month. Here is a list of carriers that support the Apple Watch:

https://www.apple.com/watch/cellular/

If you have the Cellular + GPS model and connect it with your carrier.

See Use your Apple Watch without your iPhone nearby

Perhaps ask the available carriers to support the Apple Watch. Tell them you will move your business to them if they do 😇