It's more likely that this space have the documentation theme instead of the Global Look and Feel, so the option should be on the top of the page where says: "Browse".
If you would like to have the spacetools again there, you need to choose the Global Look and Feel theme.
Because you are not in the space administrators permission.
System admin is there to let you administrate the system, not spaces. As such, you can adminstrate the permissions and add yourself, but it doesn't grant you any automatic rights over a space.
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