I run a '66 chambered in 38 Special and a '73 in 357. As already stated, OAL and the shape of the bullet determine if the gun will run smooth. Both of the toggle link Winchester designs are made to accomodate a cartridge up to 1.60 inches in length, for all calibers. In reality they work best with an OAL of 1.55". They still work OK with a length of 1.45".
There is no magazine cutoff in either the 66 or 73. The cartridge in the lifter keeps the round(s) still in the magazine out of the lifter so that the ramp on the lifter can push it back into the magazine.
Ideal bullet shape is a flat pointed one that transitions smoothly to the crimp. The case mouth needs to be crimped so there is no lip.
The 66/73s can run fast, but they need the correct ammo.
There are videos on shooting cowboy action, and the 66/73s are very common.
https://www.youtube.com/watch?v=fzGP4C9OiNE&ab_channel=3DGunner
This video does a pretty decent job of illustrating how these work and how the bullets are fed in. Initially all the calibers used in the 1873 were of a slight bottleneck design, with a round nose flat point bullet. The carrier, the brass block that lifts the shell up from the magazine tube, guides the shell as the bolt pushes the shell into the chamber.
This is my ammunition, shows the shape of bullet that I was describing.