the US will defend it's interests overseas anywhere any time

Right now Russia is warning the US not to bomb in Syria because there are Russian aid personnel in Syria and Russia is willing to declare a no-fly zone over Syria.

So the US proposal to bomb in that no-fly zone is therefore a direct challenge to Russia.

To help clarify matters the US Army Chief of Staff has given this warning:

"I want to be clear to those who wish to do us harm. The United States military—despite all of our challenges, despite our [operational] tempo, despite everything we have been doing—we will stop you and we will beat you harder than you have ever been beaten before. Make no mistake about that."

Milley also warned a future conflict with a strong adversary such as Russia might "be highly lethal" and akin to the immensely bloody battles fought in World War II.

Not a big risk of WW3 ATM, it is just brinkmanship.

Russia is far more likely to want to do the right thing in Syria since it is a lot closer to any terrorists that might develop if the state loses control completely.