You are missing only Apple research for Chateau.
But only 7 brainers in May 24th... not good (still learning ofc). For example you could've had 4 already on day one by selling the corridors.
You could've sold captured soldiers and other stuff early to get 200k occasionally for extra brainers (at the start of each month), since you can't really research more than 3-5 in reasonable time anyway. Currently you have 1.4 million worth of gold bars, which should've been invested a long time ago for brainers and another base (aka more plantations). Hellerium, Plastasteel and Superconductives for 600k more since you've already built Personal Labs (don't need more SC wire soon after that).
Go to the Fence or Research screen and middle mouse click the items to see their research tree.
For example take a look at the Highwayman. Researching it is currently gating two mission types: !Highway House! and !Bandit Business!. You want to prioritize more mission types so you can get them starting next month instead of just looking at flying ufos you can't catch. Very fast Fugitive and Hideout Search order researches are on the other hand gating Doctor X storyline missions.
Gymnastics, Church Neophyte and Church Priest are gating Neophyte Bootcamp...
Just take a look at everything's tech trees. Doing so you should come to the realization why it's not the best use of your time to devote 2/7 of your researchers to Manstopper and Holdout pistol at this point. They don't gate anything, so you are only wasting your time getting similar items. Your Airbus is loaded to the brim. Too much variety and excess amounts like 40 vodka.
You also have ton of items there which haven't been researched, so you have to keep an eye on whether they are needed for research instead of being used. Surplus amounts can be used in a pinch even if you aren't able to replace them.
If you want to see where your radar can't, take a look at the charts. Shipping activity in regions shows that there's been 2-3k worth of activity in Central Asia last month. So if you want to be surprised, fly your Airbus to western China (but keep a save first). If you anchor there for a few hours, you might be surprised by what's between Forbidden Caves and Gardens of Delight.
Here's an example video which seems to have 8 brainers by Feb 15th.
https://youtu.be/hlg4AYfubDw?t=7548