Are warnings guaranteed?

Hi. I have a question: Is there a formal rule in PHP standard library
that any function which returns false as a mean to signify a failure
does also issue a warning?

In many codebases warnings are converted to an exception by means of
set_error_handler().

Example 1

set_error_handler(fn($_, $s) => throw new \RuntimeException($s));

if (false === mkdir('/doesn/t/exist/dir')) {
    throw new \RuntimeException("can't mkdir");
}

The above code confuses a reader with issues 1) isn't the only possible
return value is now true? 2) if it throws on failure, then how can it
return anything?

One may say the checking for false return value is redundant and the
above version can be simplified based on premise that mkdir() emits
warning in all cases where it is about to return false.

Example 2

set_error_handler(fn($_, $s) => throw new \RuntimeException($s));

mkdir('/doesn/t/exist/dir');

But there is also a possibility that a built-in function fails, returns
false but doesn't issue any warning, therefore the handler set with
set_error_handler() doesn't get called and execution continues
erroneously contrary to the programmer intend of it being halted.

Looking at mkdir() documentation I can't find the language supporting
assumption made in Example 2.

The page lists two cases for which warnings are raised: "directory
already exists" and "relevant permissions prevent creating the directory".
Does it mean that in case of "No such file or directory" the function
would return false without raising a warning? It is possible as
documentation never stated mkdir() would emit warning on any failure,
just return false.

One may add a unit-test against mkdir() to the one's project codebase
proving that "Warning: mkdir(): No such file or directory" is raised
too, despite not being listed in documentation.  So far we have three
cases covered. But obviously this doesn't prove that a warning would be
raised for all failures, thus doesn't allow us to deem Example 2 correct
and replace Example 1 with it.

Is relying on warnings being converted to exceptions by error handler is
equivalent to checking return value with regards to the set of error
conditions covered? If this guarantee is already there, please point to
me to the relevant documentation page.