An article has been published last month on this topic.
Today, half a ton of satellites is falling into the Earth's atmosphere each day. It is expected that a constellation such as Starlink, once it is fully deployed, will cause 2 tons of satellites to enter the atmosphere a day. This number should be multiplied by the number of starlink-like constellations.
Two tons a day may be smaller than the 54 tons of meteors a day that go through the Earth's atmosphere. But contrary to what is stated in uhoh's answer, the amount matter that comes in from satellites is not directly comparable to the amount of meteorites, since the composition of the two is very different. The fact that the total mass is much smaller doesn't matter much if the composition is different (compare adding a ton of nitrogen into the atmosphere to adding a ton of CFCs: the effect on the atmosphere would be very different. This might be an extreme example but you get the idea). Satellites for instance contain a lot of aluminum, whereas meteoritic infall contains oxygen, magnesium and sillicates and only 1% aluminum. This means that the infall of iron would be at least multiplied by four.
each mega-constellation will produce fine particulates that could greatly exceed natural forms of high-altitude atmospheric aluminum deposition
This aluminum oxide from a large constellation of satellites could potentially disrupt the ozone layer. And aluminum deposits into the atmosphere has been suggested as a way of increasing the Earth's albedo.
More research on this topic has been published in 2023, and the answer to the initial question is in short "nobody knows".
metals that vaporized during spacecraft reentries can be clearly measured in stratospheric sulfuric acid particles. Over 20 elements from reentry were detected and were present in ratios consistent with alloys used in spacecraft. The mass of lithium, aluminum, copper, and lead from the reentry of spacecraft was found to exceed the cosmic dust influx of those metals.
So the effect of large numbers of satellites burning up at ~50 km altitude is already measurable at <19 km altitude. This is unlikely to have an environmental impact on the ground. However, we don't know how this will impact the atmosphere.
The influence of this level of metallic content on the properties of stratospheric aerosol is unknown.