This battle is invisible, even at night
I've got bad news, and I apologize sincerely... but you did tag your question "Science-Based."
Consider the distances involved: The earth's diameter is only 8,000 miles. That's only 32% of the distance from the surface to your battle. Climb a local mountain (I have) and look down on society. From even that statistically trivial distance the ability to pick out even a large building is difficult without binoculars. You're talking about the largest object being maybe 2 miles long at a distance of 25,000 miles, which means the arc length (size of the visible object from the perspective of the viewer) is an impossible to see 4.6 millidegrees. For comparison, the blazing sun is 500 millidegrees (100X larger). And, well... the entire half-degree is blazing. For some photo evidence, consider the Pyramids of Giza, which are visible from about 1,000 miles into space, but to get a feel for your distance we need to reduce the image 25X.
About 1,000 miles up (courtesy NASA):
And that same image reduced 25X:
Unfortunately, the spread of the battle doesn't help. A lot of things you can't see spread over any distance are still invisible. It would take 10,000 ships of the largest size all bunched together to be the size of the sun, and they'd have to reflect the sunlight to be seen.
Energy bursts (e.g. lasers) aren't actually visible in space. Hollywood likes to show them, but there's simply not enough material in space to heat up to show the passage of energy.
Edit: A point needs to be made here based on several comments. In a "Science-Based" scenario, nobody would use lasers or any other form of energy weapon. (a) Too hard to focus during the heat of battle. (b) The energy requirements are unbelievable. Not just unrealistic, but absolutely unbelievable. (c) There are much simpler ways to damage your opponent. And (d) you need to either generate all that energy on the spot or store it in batteries/capacitors — which means you're either economically unrealistic (oversized engine to power the weapons) or you're a big, juicy target that's easy to destroy (probably true in both cases). Remember those hoverboards that burst into flames? Yeah, now imagine a battery large enough to do significant damage to a mile-long ship miles and miles distant and your opponent is smart enough to use kinetic weapons.... The reason hyper-realistic SciFi books and shows like "The Expanse" don't show energy weapons is that they simply fail the ruthless mathematics of practicality and usefulness. Yes, given a big enough laser a hit on another ship would likely be visible to the naked eye on the ground (at least at night). But in a "Science-Based" universe, nobody in their right mind would use one.
Whether or not something like a mass-driven projectile is visible depends on whether or not it's burning during its passage—but you tagged the question "Science-Based" and wasting energy on something burning during passage rather than burning on impact is a wasteful projectile (unlikely to be used). So none of the weapon discharges are visible to any viewer. Missile rocket engines? Unfortunately, they can't be seen either, even if they're racing away from the planet (and most of the time they'd be racing tangential to the planet).
Maybe... maybe... observers on the ground, during the night, might... maybe... see a ship explode. If it actually does explode. That's more Hollywood. There's no point to vaporizing a ship when all you really need to do is stop it from shooting at you and then wait for it to be drug down the local gravity well (people would notice that). But even if it does explode: 4.6 millidegrees and a quick blip of light.
Answer to your question:
Under what conditions would a space battle involving a relative large amount of vessels would be barely visible on the surface?
All conditions not involving binoculars or a telescope and knowing exactly where the battle is taking place. And if the observer happened to see what in the battle would be a massive explosion but on the ground would be a itty-bitty blip of light, there's a high chance they'd write it off as a flashing light from a passing high-altitude passenger vehicle and ignore it.
If the sun was at the position to best cause reflections off the largest ships, they'd appear like a handful of teenie-weenie scintillating lights in the sky... kinda like the dimmest stars.
Yeah, sorry, from a "Science-Based" perspective, there's nothing here to see.