neem won't do anything... unless it has the acitve ingredient "Azardirichtin" (and that is likely misspelled, but no other word to confuse it with). If itis clarified neem, it has no avtive ingredient and just smells bad. Stick to a good wet-dry cycle can help avoid gnats, butif they come in the medium, there's not much you can do about it.
Get some bTi (bacillus Thur-somethin-or-other isrealis subspecies) ... in usa i know the brandis Summit and it is called mosquito bits or mosquito dunk. Off brand will be fine, too. The bti bacteria is the important part.
Mid-infestation, i'd top dress the bits every 7 days (must water them in with a normal irrigation) then back off to every 10-14 days once they are gone. Or, the dunks just float in a reservoir and the irrigation system takes care of it. It may take 3 weeks before you see it nearly clear up. Youcan also use the normal stuff that kills adults and kill from 2 directions in life cycle. Adults don't caue damage. Larvea damage roots.
You can use this stuff proactively, which is a good idea. I use it as a default. Early on i put bits on top, and later on there's a dunk i teabag in my reservoir, lol. It breaks down and can clog up irrigation setups, hence the mesh bag it is suspended in at water level. Or, top-dress with "bits" every 10-14 days.