I’ve even had people share a snip from some book that states this as fact

A Maths textbook.

However, this is not standardized

It's standard in every Maths textbook.

there is no reason to treat it as such just because a few people assert it is should be

The "few people" are Maths teachers and Maths textbook authors.

It doesn’t make sense at all to me that implied multiplication would be treated any differently

There's no such thing as implicit multiplication

They’re both the same operation

No, what people are calling "implicit multiplication" is either The Distributive Law - which is the first step in solving Brackets - or Terms - and neither of these things is "multiplication". Multiplication literally refers to multiplication symbols only.

It’s why that symbol is not used by real mathematicians at all. It is just abundantly more clear what you’re saying if you use the fraction bar notation

The division symbol is used - it is not the same thing as a fraction bar.

x÷y(z) is the SAME as x÷y*z.

No, it's the same as x÷(y*z).

There’s no mathematical or logical reason to treat it differently

Terms, The Distributive Law, are why it's treated differently.

2(4)^2=(2x4)^2=8^2=64

Yes, that's right. Brackets before Exponents, as per the order of operations rules.

You can’t distribute into a bracket

You know that's literally what The Distributive Law says you must do, right? Unless you have a source somewhere saying there's an exception?

Apparently you didn't bother reading any of the links I gave you, so here's one of the many textbooks which says you must distribute...

In case that's unclear, that means that 2x² and 2(x)² aren't the same thing (since 2(x)=(2x) by definition).

wolfram syntax

You know Wolfram disobeys The Distributive Law, right? I know I'm not the only one who knows this. Is that why you're insisting your way is right? Cos they're known to be wrong about this.

If you respond with more bullshiting,

You call quoting Maths textbooks "bullshiting"?

https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html

The rules of Maths that he manages to completely ignore.

This particular formula is presented in a confusing way

No, it isn't. You just have to obey all the relevant rules of Maths

implicit multiplication

There's no such thing as implicit multiplication

The parentheses step only covers expressions inside parentheses

No, it doesn't

16, is what you get by strictly following PEMDAS

except 1 is what you get from strictly following PEMDAS. If you got 16 then you missed one of more rules.

the rule is that multiplication and division have the same precedence, and you evaluate them from left-to-right

Go back and read your link again. You'll find they're obeying The Distributive Law. i.e. solve all brackets first, from inner-most out.

“implicit” multiplication

There's no such thing as implicit multiplication

follows the same rules you would have learnt in primary school

It's never that - that's how people are getting the wrong answer. In high school you get taught about The Distributive Law.

it’s (8 / 2) * 4

It's 8/2(2+2)=8/(4+4) or 8/2(2+2)=8/2(4)=8/(2x4)

Right answer but wrong reason. It's because distribution comes first

I'm building up quite a collection of these, so far from being a once-off issue. In other words, still looking for any ideas on how to fix this

Are you talking about the lack of indentation? I don't know why it does that. I tried using   with the same result. I'd fix it if I knew how!

Well, I just had an issue then here with   and eventually found backslash worked - I'll give that a go (not sure if I already tried it before).