Hi tomo pauk,
If Germany had such a surplus of machine tools - I honestly wouldn't know, but that would not be the issue.
After Hitler had cut of the German industry from its main supplier of tungsten (China) in 1938/9 a steady decline in the quality output by its machine tooling industry
(which needs Wolframcarbid/Tungsten) became obvious by 1941 - e.g. very disastrous effects on valves and high tolerance parts for its jet-engine manufacturers and as such
actually rendering its Me 262 fleet on behalf of its jet-engines as vastly useless. That a lack in skilled manpower or forced labor made it even worse is undeniable.
Regards
Jagdflieger
A big reduction in nickel content was the culprit in exhaust valves corrosion, with disastrous results on reliability for the 1st line aero engines of German production (DB engines suffering also due to not having the oil de-aerator - "Oelschleuder" - like the Jumo engines had; de-aerator was introduced by some time in late 1943). Eventually, the BMW solution to the problem from late 1942 was adopted for the DB engines.
Lack of nickel was also a problem for making durable blades for turbine on jet engines, that was circumvented via the introduction of air-cooled blades made from the chromium-rich alloy.
You can take a look at Calum Douglas' book, or his webinar discussing the rough state of availability of raw materials in Germany, ans steps taken to alleviate the problems.
As for disparity between workforce and machine tools, see for example this document; yes, not all the machines are equal. Basically, Germany in early 1945 have had about the same number of machine tools as the USA, despite having far less population.