Part of #29365.
* Replaced examples for Mul-/Div-/RemAssign with more illustrative ones
* Made summary senteces for the trait methods use third person singular
* Moved some explanations from Examples section to main explanation
* Switched around argument order for the vector-scalar multiplication
example such that the vector is on the left side (as it would be expected
if one were to switch from `*` to `*=`)
* Replaced mostly redundant example introductions with headings in traits
with more than one example (where it made sense)
* Cleaned up some examples to derive `PartialEq` instead of implementing it
manually when that wasn't needed
* Removed explicit `fn main()`s in examples where they weren't necessary
* Rephrased some things
* Added some missing periods
* Fixed some formatting/punctuation in examples