To watch Apple TV+ (even just previews) in a desktop web browser I am forced to carry an Apple "device" with me

I don't use Windows but am surprised that you need the code every time. Do you have an Android phone that you carry with you? If so, you can make it a "trusted phone number" and get the Apple two-factor authentication code sent to it. See the information on adding trusted phone numbers in Two-factor authentication for Apple ID - Apple Support

and see the following for how to request a code: Get a verification code and sign in with two-factor authentication - Apple Support

To use the trusted phone number you need to follow the instructions in the "Get a text or phone call" section of Get a verification code and sign in with two-factor authentication - Apple Support each time you want a code to be sent to your number. There isn't an option to automatically have it go to the trusted phone number instead of a trusted device every time.