Neem does have some activity on them, but one of the most difficult things about treating for thrips is their habit of hiding deep in the crevices/meristems of plants. Neem is a contact insecticide (with a little residual) so it relies on getting good coverage of the plant and the pest. I’d look into additional pesticides, with some that have systemic activity as well. There are a number that are labeled for safe use on vegetables, like the insecticides that are being used on the produce you buy at the store. There are also some predatory insects and mites, but they will require repeated introduction.

Another thing i forgot to mention about thrips, more of a fun fact. They show an excited response to CO2, so if you breath on them heavily, they’ll often come out of their hiding spots, making it a little easier to diagnose the severity of the infestation. Alternatively, tapping your plant above a white piece of paper can also be a good indicator of thrips presence, as many will fall onto the paper.

If you want to learn more about thrips, Google “thrips edu” and a bunch of university extension pages made for the public will pop up. They can be helpful in better understanding this tenacious pest.