Oh oh, one more thing that may help the long-division process seem less mystical is to realize you can stop anytime. Like, when I did the first pass and got an answer of just 30 and a remainder of 377, we could stop there!

48×30+133 = 1573

That's true. So we could say the answer is 30R133. It's just that typically we want the remainder to be below 48, because we have an answer that isn't as accurate as it could be. But there's nothing magic about going down to the zero place and not extending into the decimal places like tenths and hundredths. If we only cared about the accuracy of our answer to the nearest hundred, we could find that our answer is 30ish and be happy, and just ignore the remainder from that right away. The process of long-division is constantly about refining an answer, and gives true but maybe imprecise answers all the way along.

Viewed from that lens our answers actually went through this chain:

1573 = 0×48+1573 (0R1573)
1573 = 30×48⁺133 (30R133)
1573 = 32×48+37 (32R37)
1573 = 32.7×48+3.4 (32.7R3.4)
etc

Don't know if that helps demystify it further!