I just hit plat and im sitting with a 62% Winrate.
More trebs, and better micro on your units wins you this game.
When i was in silver/gold and people would slap a keep in front of my army to protect their base. My biggest hurdle, and seems like yours, is making sure you have the right units to defend your attack.
Preemptively make 4 or 5 springalds, as Mongals with an army this should be fairly easy, and add more trebs as you begin your assault You have 2 in the image, which will take forever to kill a keep, and never will win if they are repairing. Springalds counter Springalds, and Springalds are the only way he kills your trebs. If you see him pullin up, walk yours forward and start shooting. Even if they targets a treb or two, you should be able to wipe them and just rebuild/continue your assult.
Or you can awlays walk around the keep and hit from a new angle instead of facesmashing into it, but in the case if Berkshire, you have to take it down.
Now, on to Berkshire itself: It is a very strong landmark designed to stop exactly what you are doing, facemashing into it. Maybe the angle of the image is weird but it looks like you are WAY too close to that thing, even your trebs seem in range of it. Take it slow, build towers for vision. You are not in a hurry if he has no army. Think of how they seiged cities back then. It wasn’t done in 30min, it took literally days and weeks.
It is objectively false to say this game favors defensive turtling as a strategy. Sure, a majority of low level players default to it, but even then, they do it poorly because they just aren’t that good. The issue is that it isn’t punished quickly enough by the more aggressive players in the same bracket, so it just wins by default. Maybe Teamgames are more turtley, but this sounds like a 1v1 situation.
With the repair cost changed to stone, and the overall stone reduced in a revent patch, making normal keeps is nich less powerful than before purely because the sustainability isn’t there. Very few games at the higher levels go into imperial, and if they do, it isn’t very long before the game is done anyway.
More barracks/stables so you can replensih your army as it dies. Build units AS your old ones die in the attacks, not after they are gone. Keep the pressure on, and eventually they will crack. Think of it like breaking a diamond, not an egg. Constantly increaseing pressure slowly, not swiftly smacking it once.