Mystery Clog & Backup in Upstairs Bathtub
Based on your description and what you have snaked, it appears that the blockage is in the down-pipe between the first and 2nd floor.  Water is traversing horizontal and able to back flow into the tub. I don’t know why the plumber didn’t do this, but if you can safely do this, look for the sewer vent pipes on the roof above the area where the blockage is.  You should be able to snake from the vent pipe to the down pipe and clear the blockage.
Before doing the snake from the vent pipes on the roof, You might try the chemical method first, such as Drano Gel and Main Line Clearners.  As always be careful while using the toxic chemicals.