Latest news from Russia (and I got this presented as facts - from a person who ought to know better):
It's not the Russians that prevent people from leaving Mariupol, it's the Ukrainians. They are shelling their own population in order to win the propaganda war. Their army place military equipment by hospitals on purpose. They use civilians as human shields, preventing them from leaving military targets.
For someone on the outside of Ukraine - hell, even for someone inside Mariupole - it can be hard to see what's going on. Of course the Ukrainians are blaming the Russians for breaking the ceasefire agreements, and of course the Russians are blaming the Ukrainians. The fault may be entirely at one or both sides, and neither me nor you can know for sure. I read a headline the other day that the Russians had been putting mines on the roads they suggested to use as "humanitarian corridors". Well, if it's true that there are mines on the roads used by the people evacuating, then who knows who laid them there. I don't believe the Russians would intentionally send civilians into such a trap.
I think that the claim that Ukrainians are shelling their own population to win a propaganda war is just too outlandish to be taken seriously. It defies all logic. For one thing, the Ukrainians are winning the propaganda war every day, they don't need to do such desperate things. The risk that such a move would backfire is huge. Such an operation would require not only a single person but lots of persons to perform atrocies towards their own population - women and children that are already suffering from lack of drinking water, food, heat and hygiene - and not only that they have to perform such atrocities, but they also need to keep it secret for all the future. Well. There is the Stanford Prision experiment showing that it is quite possible to divide the population into the armed population who are exercising power and having sufficient amounts of food, drinking water and heat - and the rest of the population being abused. But still - with limited resources it would even be good to get out children and women. Extraordinary claims requires extraordinary evidence. When googling on this claim, the only thing I can find is from the Russian Tass, citing claims from a DPR military commander that civilians were forced to stay in the basement of a school and not allowed to leave. The news story has been parroted by some Syrian news outlet. That's hardly credible - and it's also from the 3rd of March, so it's already old news - and it may even be legitimate reasons for disallowing civilians from leaving a bomb shelter in the middle of a bombardment.
It's a bit more difficult to dismiss the claim that the Ukrainian army is intentionally putting military hardware nearby their hospitals. It could be true and it could be false. I would tend to side with the Ukrainians here, they are the defenders, Russia is the aggressor, if the Russians cannot take out the artillery without bombing hospitals, then they shouldn't shoot in the first place.
We've actually seen videos of the usage of "civilian shields" - flag-waving unarmed civilians standing up against the military, visibly demonstrating on the streets of occupied towns and cities, attempting to protect the nuclear plant from the invaders, etc - but there are no indications that they do so against their own will. Googling on it, I find an article in an Indian news outlet that is citing RT that again is citing officials from the Russian Defence Ministry, claiming that 2.5 million Ukrainian people are held hostages as "human shields". Hardly credible information. Reading further, the claim is that the Russians have a database of 2541367 people who wants to evacuate from Ukraine to Russia, but is prevented to do so. I seriously doubt it's true, but even if it was true - those people are hardly "human shields", they are not held against their will at military facilities, and I also think it may be legitimate to prevent civilians from exposing themselves from crossfire at the front line.
Image credits
The photo was found at Wikimedia Commons, Mvs.gov.ua, CC BY 4.0 and shows civilians being evacuated from Volnovakha in the Donetsk region, at the 3rd of March.