Two issues - first, how are you going to get the cistern in the basement? A lot simpler to put it in the yard, where you can use heavy equipment and any repairs or leakage issues can be fixed. Locate it away from the house and reduce the risk that your first indicator of leak is water in the basement.
Similarly, pump failure can also result in overflow into the basement. Depending on the sooil, would that water saturation also endanger the integrity of foundations?
Then the bio-growth issue- better to have an odor outdoors than indoors.
Finally - will your town allow it? If you are on the local water supply, they may restrict watering during droughts. “But I’m using grey water” you say. So what? If Fred down the street wants to have a nice lawn and flowers, and doesn’t mind paying for the water, he just runs the kitchen tap until the grey-water tank is full enough to water. How do you guarantee the grey water is legitimately and not wastefully greyed out? They MIGHT let you get away with a totally separate rainwater-only system, but still - how do you stop someone from running the garden hose into the tank at night? And how do neighbours know that they don’t have to report you because your system is legit?
Install a discrete water seepage system for watering; but even then the greenery will be a giveaway.
As to whether the water is sfe for plants - depends what you wash down the sink? If you are a heavy soap user, it may not be good; ditto detergents. Perhaps to clean the system out, you may have to drain the tank and hose it out from time to time - which means either carefully regulating use, or flooding the neighbours or storm sewers. Plus - what is grey water? Obviously not toilet waste; but do you wash cloth diapers in the sink (after initial cleaning) or anything else disgusting?
then you have to repipe the waste system to separate the grey (bath and sinks, aloundry…) from toilets. A lot of work.
The devil is in the details.