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Specifically, I know that Krieg contributes a massive amount of troops to the imperium, so I’m wondering if the loss or destruction of Krieg would have a noticeable impact on the ability of the Astra Militarum to fight?

Less than Cadia's destruction did. So none, really.

Honestly?

Virtually none. Krieg remains but a single planet. And likely isn’t the sole world using cloning to provide troops.

In a galaxy spanning empire like the Imperium, a single planet might help decide the fate of a system, perhaps even a subsector, but its trivial when compared to the countless quadrillions of human lives spread out on a galactic scale. The loss of a single planet is offset by the reconquest of another, settlement of a new one, construction of new manufactora elsewhere, etc.

Of course, the Imperium would be a magnitude less grimdark without those dour fellas.

Its destruction would mean both nothing and something. Krieg is noted for its ability to produce insane numbers of well-trained troops for the Imperium's battles, 50 million a year according to Lexicanum. The cult of sacrifice that drives the Krieg to battle makes them some of the most loyal and dependable troops the Imperium has to offer. There is even a short story of a Krieg soldier left behind on a world after a war who attempts to lead civilian life but is so driven by his need to serve he enlists when the planet founded a Guard regiment.
But as others have said the Imperium is so vast that it could go completely unnoticed.
However, a planet as famous as Krieg would do damage to morale just as the loss of Cadia did.

Itll just hurt me... a Guard players heart a little more.