On the Galactic Map, under the 'Filter' dropdown towards the bottom, there is an option called "Strength (All)". This switches the display from the COUNT of ships to the STRENGTH of the ships. Strength is a rough estimate of how strong a particular unit is. It's only a rough estimate, because special abilities, multipliers, immunities, etc, all play a big role in adjusting exactly how combat effective a unit is.
But Strength is the base estimate, and it is the estimate the AI uses in its own calculations.
Also on the Galaxy Map, under the 'Displaying' dropdown, there is an option marked "Detected Threat". I suggest you find or set a shortcut key for this option, as you'll want to use it a lot. It changes the ship type filter to show those AI units that are currently not guarding anything and looking for a way to hurt you. Note that Threat ships and the Threatfleet are not the ONLY behavior of AI ships that will go on the attack - they're just the most common.
Combine these two options to figure out where and much deadly the AIs units are.
In your game, the Desme system has 167 AI ships as Threat, with a strength of 1616. Your fleet in Maisido is about 350 ships for 1900 strength. The AI usually won't attack where you are stronger, and it is (now) smart enough to look at systems near the target system to see what human reinforcements can be quickly brought to bear. It used to not bother, which led to a lot of trickery with hiding reinforcements on the other side of a wormhole and easily ambushing the attackers, so now the AI is smarter.
However, when you move your fleet to Dihararran, they aren't in position to defend your Homeworld anymore. So the AI only looks at the defenses on your Homeworld itself. And those are... very minor. Only about 5 or 6 of each turret, and not even 20 mines. That's about 350 strength. As you can see, when the AI realizes that it is about 4 times stronger than you, it quickly attacks.
My recommendation is to quickly build more turrets. You've already unlocked the Mk II Needler and Missile turrets as well as the Spider turrets, yet you've only built a few of each. Build at least 20 of each. Even more distracting, you've unlocked the HBC Mk Is, yet don't have any defending your Homeworld. I suggest you build out ALL the Sniper, Spider, Mk II Needler, and Mk II Missile turrets on your Homeworld, and then add 10 of your HBCs as well.
This pushes your HW defensive strength up to about 4000 or so. Enough to keep the Threatfleet off your Homeworld, or smash it if it does attack.
It may not be obvious, but most Turrets and Mini-Fortresses have per-planet caps. How many you have on one planet does not impact how many you can build on other planets. So, defend your Homeworld well! Lose it, and that's Game Over, so be careful rather than sorry.
HBCs, Tractors, Mines, and Grac turrets have global caps: For those defenses, it does matter how many you've built elsewhere.