1) A vaguely-argued upper bound.
This turns out to be a surprisingly common problem for providing answers here, and I have yet to find a good value.
In The logistics of corpse disposal I gave 45 degrees, arguing that "Most stuff is lower, I know nothing that's steeper, and steeper means fewer bodies, so 45 is likely our worst case.". I feel this is a decently defensible upper bound.
2) A spherical-cow lower bound.
While, as others have said, the exact value may be hard to calculate, we can also at least establish a lower bound, by establishing a precise value for the case of a zombie spherical cow, which we shall presume to be frictionless except against the ground, and incompressible.
This works out at 23.8° (via https://eng.libretexts.org/Bookshelves/Materials_Science/TLP_Library_I/33%3A_Granular_Materials/33.4%3A_Angle_of_Repose).
That's reasonable as a lower bound, though as Nosajimiki points out, kinetic effects of people walking on them may mess with that.
However, as I understand the angle of repose, it's the angle of stable rest. Than angle of dune sand where you can walk down a sand dune and NOT cause an avalanche of more than the sand you displace. It's the angle of the bodies where you can scramble over them and not cause their sliding about to amplify and cascade. So I'm unsure whether this would actually have a significant effect.
Every assumption we made (spherical, incompressible, frictionless), reduces the angle of repose, so we can reasonably round up and still call it a fair minimum angle.
That still leaves us with a range between 25° and 45°. We could split the difference and call it 35°, perhaps, as a reasonable guess.
However... we don't need to guess.
We can try a PRACTICAL EXPERIMENT!
You didn't expect to find that in an answer, did you? And, OK, I'm lying. But I can at least simulate it.
Most computer games have decent friction, gravity, collision, and rag-doll physics, nowadays. So what's a game where I can create a gajillion corpses and let them just... pile up?
3) UEBS II, 1,000 modern soldiers
Ultimate Epic Battle Simulator II (UEBS II) might be able to handle this. I note that it has a checkbox for "volumetric blood" with the note "can drown units", so this is clearly expected to handle LARGE armies.
It lets me set 1 million regular zombies to attack a thousand modern soldiers. I placed the zombies in four groups of 250,000, to surround the soldiers... OK, the soldiers died fast.
4) UEBS II, 1,000 super-soldiers holding their ground
Let's make the soldiers be ubermensch, have ten times the firepower and ten times the health, as well as a 50% chance of blocking melee attacks.
After massacring 1,000,000 zombies, which took quite a while at about 300 zombies a second, I see that the angle of repose in this game is 26°. But I'm skeptical: in this game, this feels a deliberate effect, that they've engineered. They may have just picked a value that "looked right". On the other hand, it does look right.
Also, your suspicion was correct. I set the 1,000 supersoldiers to hold their position and fire, on the side of a gentle mound. Initially, it mattered: the zombies coming over the mound could only be fired at when they crested the rise, so they died much closer to the soldiers. On the other side, there was a significant distance that could be shot, so the zombies were kept well away.
But as the bodies built up, this stopped being an issue, as the bodies themselves made a mound, which advanced towards the soldiers as the zombies fell. Eventually, they were in the dip at the top of a pyramid, surrounded by mounds on all sides. The soldiers killed them all, but took heavy casualties, with little more than six hundred of their original number remaining.
(26 degree angle of repose: this looks about right. If you placed a body on there, you wouldn't expect it to slide to the bottom, but you could imagine it doing so if you gave it a bit of a shove.)
5) UEBS II, 1,000 super-soldiers, moving tactically
Setting the soldiers to attack instead of hold their position, they were able to scale the sides of the body-berms and shoot the zombies as they approached up the pile. This resulted in a differently shaped pyramid, with the berms becoming a ring around their original position, expanding outwards rather than constricting inwards as it had when they'd held position. This meant their lines eventually became too thin to hold back the flood, so they had to retreat once the zombies broke through, and defended just one side of the ring, making the top of their pyramid lopsided. As that side rose up, they eventually recaptured the lower side of the ring.
Rather than losing a third of their number, they lost only two out of a thousand men. This approach was clearly better, tactically.
6) TABS, 1000 halflings vs 1 dragon
Totally Accurate Battle Simulator (TABS) is on sale in Steam as I write, and is much cheaper than UEBS II anyway. It's for much smaller-scale battles, but with a fight on a slope, I was able to get some confidence in the the angle of repose from just 1,000 halflings, though that gave me a framerate around 3 fps.
The angle of repose in this game is just 11°! But watching the fall and slide into place, I am once again skeptical. I think it has them being VERY slippery. This would be the AoR of something like wet liver. Or perhaps the ground is slippery, and the slope they are on allows the ones at the bottom to slide sideways because of the sideways pressure from those on the ramp. Maybe testing on a ramp was a bad idea, but it was the only way I could find to make it work.
(11 degree angle of repose: this just looks too shallow. If you put a body at the top, it feels like you wouldn't be able to shove it so it slid to the bottom.)
Overall, then, my idea of simulating it fell short, but did highlight some of the variables. I didn't expect friction to be such a big deal, for example.
In the end, you'll likely have to pick a number. UEBS' angle feels about right, viscerally (ahem), and I do feel anything much steeper would look weird and unstable.
I heartily recommend using a simulator like these (UEBS II in particular), to get a sense of what your battle would be like. I'm not affiliated with either of the games, but did buy them for this question (Yes, I spent $29 after tax on trying and failing to answer this question. Shut uuuup!), and it was eye-opening in various ways.
At 300 dead zombies a second, that results in rivers of bodies flowing down the outside of their corpse-pyramid. Everyone gets spattered in blood. Of course, it's simplified: the soldiers aren't harmed by their own bullets and have perfect target-acquisition skills, etc. And blood does drain out of bodies, so the "volumetric blood" option may be an eye opener, though I suspect it's considerably less than realistic.
Well worth setting up a simulation of it all, anyway.