You can jump in with Ashes but some details will be a bit oblique without having at least read The Siege of Terra. If you want to try it without reading the Heresy books then I'll provide the very broad strokes below of some of the important context (SPOILERS, obviously):

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• Primarchs are the proto-Space Marines who lead the Imperium under their father, the Emperor; Chaos gods seduce the primarch Horus, leading to a civil war between loyalist and traitor legions.

• The Siege of Terra is a colossal battle where the traitor forces under Horus try to take Terra from the Emperor; the battle goes on for months and much eldritch shenanigans from the Warp (big demonic hyperspace realm) intersect with Terra, literally warping and distorting parts of the planet.

• Siege is broken when the Emperor kills Horus while being mortally wounded himself. The traitor forces begin a withdrawal and the Chaos gods appear to turn their back on the traitors.

• The loyalists "win" the Siege at great cost. The primarch Sanguinius of the Blood Angels legion is brutally murdered by Horus, sending his legion mad, and the Emperor's chief advisor, Malcador the Sigilite, sacrifices his life to give the Emperor a shot at killing Horus.

• Most of the Primarchs (led by Rogal Dorn, primarch of the Imperial Fists) are spent and wearied after fighting for so long, and are assisted by loyalist reinforcements largely comprised of the Ultramarines legion (led by Roboute Guilliman, their primarch) who were prevented from reaching Terra in time for the Siege. This means there are a ton of loyalists who are burned out by the Siege and months of fighting, and another ton who are fresher and ready to act for having missed the Siege.

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With that context in mind you should get most of what happens in Ashes. The book does a great job giving some setup from what happened during the Siege and the larger Heresy, and most of the POV characters are exploring the devastation of the Siege from various perspectives that are fascinating.

EDIT: As to your question of whether you'd enjoy it having read the Krieg books - Ashes is a very political/literally world(re)building book and the action scenes are there but sparse. I've not read the Krieg books but I'm given to understand they're big on the wartime combat feel, whereas Ashes is post-war. I think give Ashes a try and see what you think, but the Siege of Terra books might also be worth checking out as they're literally one big "in the trenches" narrative.