Very disappointing statement to hear from an engineering student (said as a career engineer myself. Study internal ballistics for powder gasification, combustion, and bore pressure curves for about 20min some day and you will see the fallacy in your statement.
Powder is gasified early in the bore, then the gases are combusted as the bullet travels.
The combustion reaction converts a relatively high density solid powder into a high pressure gaseous mixture. The “instant the powder is burnt,” the bore behind the bullet is full of high pressure gases - as you’d realize as an engineering student, pressure is a force applied over an area, and in our particular physical system, the bullet will remain accelerating (albeit variable acceleration) any time the force behind the bullet exceeds the friction of the bearing surface on the bore wall plus the relatively infinitesimally small inertia of the air in front of the bullet. So no, the moment the powder is burnt, the bullet does not start slowing down. The powder is burnt, it remains a high pressure system on one side, unbalanced, such a net outward force remains until the expansion is satisfied. PV= znRT at that point....
ETA: so your free body scribbling isn’t necessarily incorrect, but your basic understanding of when the propelling force of the system declines is the problem.