I've investigated a bit why that test with mixed~numeric-string doesn't work.
After using is_string mixed actually turns into string, and then PHPStan need to subtract numeric-string from string. It doesn't work, so I've removed the test.

Actually, it's a hard problem.
At first I've tried to express it through string&mixed~numeric-string, but I got an infinite loop while running tests.
Then I tried to implements SubtractableType on StringType, but TypeCombinator::intersectWithSubtractedType() can't intersect two SubtractableType properly in some cases. In some tests subtractable type was just dropped for some reason.
E.g. this test:

			[
				new Expr\BinaryOp\BooleanOr(
					new Expr\BinaryOp\BooleanAnd(
						$this->createFunctionCall('is_string', 'a'),
						new NotIdentical(new String_(''), new Variable('a')),
					),
					new Identical(new Expr\ConstFetch(new Name('null')), new Variable('a')),
				),
				['$a' => 'non-empty-string|null'],
				['$a' => 'mixed~non-empty-string & ~null'],
			],

becomes just mixed & ~null in $context->false(). Unfortunately, I wasn't able to investigate it deeper.

I tested the mixed~numeric-string case locally and I think this works now after #1656 got merged, when the change from this PR is applied.

my local test:

<?php

function foo2(mixed $s): void
{
	if (!is_numeric($s)) {
		\PHPStan\dumpType($s);
	}
}

php bin/phpstan analyze test.php  --debug
Note: Using configuration file /Users/staabm/workspace/phpstan-src/phpstan.neon.dist.
/Users/staabm/workspace/phpstan-src/test.php
 ------ ---------------------------------------------
  Line   test.php
 ------ ---------------------------------------------
  6      Dumped type: mixed~float|int|numeric-string
 ------ ---------------------------------------------

@fluffycondor please give me a ping in case you won't have time to finish it and I should push it over the finishing line

Thank you!