That depends on the text app you are using. If you are using Verizon's Message+ (the red & white icon) I think it has a backup option built in to backup your texts to Verizon's cloud storage so you can download onto your new phone. I think so.....I haven't used Message+ in years. If you use Google's Messages (the blue & white icon) there is no backup / restore option, never has been. There are many apps on the Play Store that can provide backup & restore functionality. SMS Backup&Restore is one example, it works great & it's free. You can backup your texts to your Google Drive cloud storage > download the app on your new phone > restore from the saved backup.
Hope that helps.
Great job, Scott5337. You are right on the money. For additional information on how to transfer text and all of your other personal data to your new phone, you may review the link here: https://support.google.com/pixelphone/answer/7129955?hl=en
Being able to transfer your messages between devices is crucial. There are a few factors that can impact this. Are you activating a Pixel 3 as a new phone from a Pixel 2 before? What messaging application are you using?