There is a lot to unpack here, but there is a short version.
"Shouldn't BTO the same for every projectile?" Yes and no. Bullet quality can be the state of the art, and yet there will be variation.
"Same chamber" the chamber is not part of the discussion since now you would be discussing jump versus jam.
You could have an equally lengthy discussion on what constitutes a dimension to touch.
If you imagine the tools you are using, versus the very shallow contact angles where you are trying to contact or seat bullets...
Now consider tolerances, friction forces, etc.,
If you handed five different proficient technicians the same hand tools, and just one bullet, there would be a spread of results.
It is not hard to imagine that the measurement contact force can be perfect, and yet the friction between the bullet and the tools still has an effect.
Now add in the less than perfect contact force, and your results start to scatter more, and that is with just one bullet.
After all, you are jamming a pointy curved surface into a little hole (the tool), so it can wedge in differently every time. But with some experience, you can learn to get less variation by practicing with just one bullet over several sessions.
Even if you were to use the exact same diameter and contact patch on the bullet's ogive, you would find variations just due to friction.
While it would be ideal to use a measurement tool (anvil) to make the bullet measurements at exactly the same diameter as the gun's touch points, having a difference in those diameters and contact areas is not the only reason you will see variation. Even the seater stem probably uses a different contact area and diameter. (It isn't the end of the world.)
Now add in the concept that there is tolerance to the bullets, the materials, and your tools versus the barrel are probably not using the same place on the bullets to reference, and you can begin to understand that this is a complicated discussion, but we can simplify it by saying we just need to be consistent with our process and trust that comparative measurements in this context are going to be nearly as good as absolute measurements where things are perfect.
The next step after accepting how difficult it is to just check bullets as a component, and how friction and contact forces make this difficult, now add in the seating force variation due to your case prep and workmanship. There can be a significant difference between virgin brass and cycled brass just due to friction differences in the neck after firing.
The measurement tooling doesn't need to be an exact copy of the gun, nor does the stem of the seater in the die. It helps to have good quality tooling, brass, and bullets, but you can master your loading without trying to turn your measurement tools and seating dies into a copy of the gun's touch points.
It takes some dedication and attention to detail to minimize the workmanship parts of the above discussion, and yet there would still be bullet tolerances and friction involved, and that means you will rarely see the variation in a real world BTO value get below 0.003" unless all the planets are aligned with the components and the hands of the loader.
Check to make sure you are using the correct fit in the seater stem. Practice with a single bullet over and over. Pay attention to your brass prep and neck friction conditions. You will get better. YMMV.