Is your t-spine stiffness a new or ongoing situation?
Yes, you could be experiencing more stiffness as you are changing your posture. You are breaking a habit and forming a new one. You are using different muscles/tissues to maintain your improved posture and all the muscles/tissues may not have been used to the same degree. New work for some of the muscles/ tissues involved. Take breaks to reset your position throughout the day.
As this improved posture becomes your default posture it will improve.
Keep working on it.
Are you working up/downstream?
Traps?
A couple to mix in.
Tuesday, July 16th, 2019 – T Spine Overhead Restorativee
Friday, November 23rd, 2018 – T Spine Scrub to Improve Your Overhead
Basic T-Spine Mobilization
T-Spine Plate Smash

Doing a morning basic shoulder spin up (click the arrow on the right to the 4th video) may help.