My new Pixel 5, that I just got last week, transferred everything from my Pixel 3 just fine using a cord & using the same SIM card.
Text came through with contacts name and picture but I had to reset the desired notification sound for every single contact.
My problem was every incoming phone call was displayed as "Restricted". Went through all the settings, googling for a fix, and visiting the Verizon store (complete waste of time) the only resolution that was mentioned was to hope and wait...... 4 days later, It finally started working. I believe it was a Verizon issue not supporting incoming caller id numbers and/or pairing them to my contacts.
Now that everything is working, I am thrilled I snagged a Pixel 5.
Now I can wait for Pixel 7 or more likely 8 when they finally get smart and make a smaller size phone like the 5!