We do know the size. And I was wrong with how well we can measure the parallax. But other than the parallax the explanation was still mostly incorrect as far as I can tell.

> Your brain can calculate distance because of the parallax that you get from having two eyes.

This only works for stars that are very close to us, not for most of the stars we see.

> Or you can see that people look smaller when they are further away (assuming you are familiar with the average size of a person).

If you use average size you're going to have a large error. You need to know how large the star actually is to determine how far it is. You can't just assume all stars are the same on average because we know that's not the case. Also I assume you're actually talking about apparent and absolute magnitude here.

I'll just add that this can be part of the puzzle when using dynamic paralax, but it doesn't work as you have worded it.

> Imagine these same principles applying to different positions in orbit around the Sun throughout the year

Yes, parallax works like that. But you will see no change in brightness of a star on our orbit.

> type 1A supernovae, and red / blue shift of light

Both of these are used for measuring distances to other galaxies. You can tell how far a Ia supernova (standard candle) has occured. But if you happen to see one from our own galaxy, you just know there was one binary star there but generally we just look at a bunch of galaxies and hope to see one there. But you probably didn't even know there was a star there before so you can't use that to measure stars you actually knew about.

red blue shift can tell you distance only of galaxies outside our neighborhood. You can't use it for measuring distance of stars that are next to us.