I have a Samsung S24+ and Lenovo laptop with WIN 11, so we're very close in equipment. I have never been able to delete anything from the WIN side, nothing. I can originate or reply but delete, as far as I know, is only on the phone.
I have found that anything on the phone side of Phone Link that is in Spam and Blocked or Archived will still show up on the WIN Phone Link with other messages, like they never left.
I don't know what the political texts are but I have been able to delete anything from the phone side of Phone Link and that eliminates them from the WIN side of Phone Link. I think you may be using the default SAMSUNG MESSAGES app that came with the phone. If so, go to the Play Store and download GOOGLE MESSAGES, then make that the default messaging app. (Your current messages will be visible in the Google Messaging App.)
Then open it and look for the small "face" on the right side, click on it and it will take you to the menu where you can access the Spam and Archived messages. Go into each section and delete the ones you don't want.