My two cents worth about it:
Sorry to say that, but IMHO - simply and straight forward - forget it !
@Steve has shown in his comparisons with the Z180-600 that this lens doesn't like TC's very much and if you take a look to the
review at Photogrphylife , you'll see that the lens already shows a slight drop solo at 400mm (which isn't critical though), but with 2x you loose more than 40 % of the resolution and you are at f11 wide open. This is not what I would call a lens anymore, because you are not only hampered in terms of IQ but also in relation to lighting conditions (--> Shutter speed / ISO) and object isolation (DOF).
Honestly, for the Z Tele zooms I decided to forget about TC's completely, being it for the Z 100-400 or the Z 180-600. If I need to get more reach I simply need to use another lens or - as a compromise - I accept to crop, because with this kind of quality loss introduced by using a TC the result with cropping a FX image shot at 400mm without TC might be just as good if not better. And to put this in context, this is not a really bad news.
Just take a look at what stunning mouthwatering images have been taken with cameras like the D4s in the DSLR days - with 16,2 MPixel !
I don't know which camera you are using, but assuming it would be a Z7 (II) , Z8 or Z9, if you shot in DX mode or made a crop to DX format in post you still have about 19,4 MPixel resolution left and this is about 20% more than the D4s had and just 6% less than a D5 or D6, and nobody would seriously argue about the fact, that they were pro grade bodies and the flagships of thier time.
If you like using zooms and wish to have more reach, then take a look at the Z 180-600. Considering that it costs about € 800,- more (sorry for the Euro but you get the idea) than just the two Z TC's together and at the same time gives you zoom flexibility, handoldability and IQ on a decent level with 200mm more reach, I am pretyy sure that this will most likely make you happier straight away and keep you happy in the longer term also.
I have them both for exactly the reason I pointed out above. I love having the flexibility with zoom lenses, but it is more or less a given, that most of them do not like TC's. Thus, if I have them both with me, I use the Z100-400 up to about 350mm and then let the Z 180-600 take over.
But the overlap in focal length range often makes ist easy to decide which one to take for what I want to do, if I have to go small/light and accept some compromise in IQ at the short or long end - but in a much, much smalller scale than I would have to accept it with using a TC's.
And there is something else that tends to be forgotten. Theoretically you use the TC only when your lens gets "too short". But if you use the zoom for its flexibility, in most cases people tend to have it mounted more or less permantly in a particlar situation giving you e.g. a 140-560mm lens with the TC-1,4x. But this comes at a price: The drop in IQ quality then applies to the entire zoom range and you end up shooting with maybe half the IQ you'd get with the lens solo at the same focal length - forgetting about loosing one or even two stops of light by using a TC.
As in many discussions around IQ, SNR etc. it always comes down to the same thing: "You can tweak data and write clever software to do it, but you just can't cheat of bypasss physics".