As already brought up the 70-300mm lens is not a macro lens by any measure. I would not even recommend using extension tubes with it on a Z-mount camera simply due to the fact you would be doing a double-adapter stack. It might work, but you double the amount of possible ways it could fail. Extension tubes on an F-mount camera, I say not a bad thing to do since it is only 1 "adapter" in play.
I don't know if you are still using an older F-mount body in addition to the Z5 (I do that). If you are just using the Z5, really consider saving for Z-mount lenses instead of picking the low-hanging fruit with F-mount. It will reward you for years to come.
My opinion: the Z105mm micro is the best option, but it is not the only option. Check with stores, it is currently is sold with $100USD instant rebate in the USA this month, and I expect some similar deals in world markets also. The lens also shows up from time to time used, but not that often due to being a fairly new model. But there are some Z-mount aftermarket lenses out there. Manual focus mainly, but also lower cost for sure.