> So I didn't know that when I press backspace in the terminal, "x08" is being sent, not "^H".

"0x08" is "^H". H is the eighth letter of the alphabet. There is no difference between those except for the notation. In the ASCII character set, the first 32 characters are called control characters. This is why many keyboards have ^ on their control keys. The 26 control codes 1 through 0x1A correspond to ^A through ^Z.

PS This relates to the 7-bit ASCII character set, American Standard Code for Information Interchange, composed of control characters for communication control, letters, numbers, and punctuation.

Pretty sure it's for the human, yes; how else would you represent "hey human, something just echoed the thing you get from ctrl-h"? (Keeping in mind that this almost certainly predates unicode and fancy fonts, and probably colors in the terminal. I'm open to the idea that we could do better today, but it's hard to overcome 50 years of tradition.)

Usually that’s rendered as one control unit not as caret + H. The caret indicates an escape character. You can typically type in escape sequences via ctrl v (eg ctrl-v + tab for the tab character instead of tab completion)