The Pixel's Messages app has been buggy for years for international users with two SIM cards/two numbers with different country codes. I have owned multiple Pixels over the years, and they ALL had this same bug. It's been reported countless times, nothing has changed.
It ignores the systems preferences for which "line" or phone numbers is set by default and randomly uses the other number which involves international fees when sending messages to a recipient with a different country code. It doesn't matter how you set it up, it will ignore your settings.
There is no way to set it up to automatically choose the right phone number depending on the recipient's country code. For example, when I send a message to a US recipient, I obviously want to use my US line. But no, it randomly uses other numbers (even when the US number is set by default, as stated in 1).
I can understand that automatically choosing the "right" number may not always be what the user wants. But arguably, this is what the user wants most of the time, so there should at least be an option for it. If I have a US number and a German number, I'd like to have the option to select the right sender number depending on the recipient's' number. People in the US are more likely to know my US number, people in Germany are more likely to know my German number, and this will avoid international fees to send across country numbers.
I hope to see this bug fixed in the future. In the meantime, international users should probably use iPhones.