I have a shooting bud who accidentally fired a 270 Winchester round in a 300 Win Mag M70 claw extractor rifle.
Case head ruptured on the 270 Win cartridge. Entire left side of his face was bloody from brass and gunpowder particles, his left eyelid was closed so he did not loose sight in that eye. He was fortunate that he did not lose his right eye, his right eye was protected from debris by the scope bell. Scope was bent/deformed. The Mc Millian fiberglas stock came out of it without splitting. Floorplate was not blown open. The action was headspaced and found to be OK. The rifle is back in use.
Now the primary differences between his bo bo and yours was cartridge diameter. The case head of a 270 Win is less than that of a belted magnum. Brass case sidewalls will rupture when they stretch too much. In your rifle, the sidewall difference was not enough to burst the case, so, lucky you.
If you had chambered a 338 or 35 belted magnum in your 300 Weatherby, that would have created a bore obstruction and the end result is unpredictable.
I shot about 100 6.5 Swede cartridges down a 7.5 French MAS to fire form the cases. The 6.5 Swede shoots a smaller diameter bullet and the neck is a little longer. All I had to do after firing the rounds was trim the case necks. The rifle was not damaged in any sort of way. Accuracy was horrible, but, I wanted fire formed brass.
Don't worry about your rifle. Pressures were way below that of a 270 Weatherby or a 300 Weatherby because you fired a bullet smaller than the bore.
Now if you had fired a bullet larger than 30 caliber..............