Some other pedantic notes you may find interesting

It's hilarious that you added in this in afterwards, hoping I wouldn't see it so you could claim the last word 😂

There is no “correct answer” to an expression without defining the order of operations on that expression

There is only one order of operations, defined in many Maths textbooks.

Addition, subtraction, etc. are mathematical necessities that must work the way they do

Hence the order of operations rules, found in Maths textbooks

But PE(MD)(AS) is something we made up

PEMDAS actually, and yes, it's only a convention, not the rules themselves

there is no actual reason why that must be the operator precedence rule we use

That's why it's only a convention, and not a rule.

this is what causes issues with communicating about these things.

Nope, doesn't cause any issues - the rules themselves are the same everywhere, and all of the different mnemonics all work

Your second example, -1+3+2=4, actually opens up an interesting can of worms

No it doesn't

so subtraction is a-b

Just -b actually

negation is -c

Which is still subtraction, from 0, because every operation on the numberline starts from 0, we just don't bother writing the zero (just like we don't bother writing the + sign when the expression starts with an addition).

a two-argument definition of subtraction

Subtraction is unary operator, not binary. If you're subtracting from another number, then that number has it's own operator that it's associated with (and might be an unwritten +), it's not associated with the subtraction at all.

you can also define -1 as a single symbol

No you can't. You can put it in Brackets to make it joined to the minus sign though, like in (-1)²=1, as opposed to -1²=-1

not as a negation operation followed by a positive one

The 1 can't be positive if it follows a minus sign - it's the rule of Left Associativity 😂

These distinctions are for the most part pedantic formalities

No, they're just you spouting more wrong stuff 😂

you could argue that -1+3+2 evaluated with addition having a higher precedence than subtraction is -(1+3+2) = -6

No, you can't. Giving addition a higher priority is +(3+2)-1=+5-1=4, as per Maths textbooks...

Isn’t that interesting?

No, all of it was wrong, again 😂