Are Charnel Grounds still a thing?

No modern, industrialized nation still uses anything akin to charnel grounds, mainly because they have turned the disposal of corpses into a highly regulated industry. Corpses within densely populated urban societies are a significant health hazard. Even within moments of pressure (such as epidemics with high fatality rates) industrialized nations prefer mass graves to open-air cremation or natural decomposition. Mass graves preserve a minimal sense of dignity for the corpse, where fire-pits would appear as an act of panic or an all-too-visible symbol of despair.

Certain tribal groups still maintain open lands designated for cremation or open-air decomposition, most notable Indian and Native American groups. These would technically amount to charnel grounds, although — because of the prohibitive cost of funereal pyres in India, and the relatively sparse populations of traditional Native Americans — they don't see excessive use that might be hazardous or disruptive to surrounding communities.

There are, interestingly, body farms where researchers study the decomposition of human remains under a variety of natural and artificial conditions. Research considerations aside, these farms do roughly resemble charnel grounds.

You could always work at a morgue. In america there are corpse farms where crime scene investigators practice their skills.

I wonder in how far the burning of human corpses in the open is still a thing?

Ideally looking for a place where there are always burnings and corpses and mourning.

More active than ever been, look at Eastern Ukraine, plenty of burning of human corpses everywhere, on the streets, inside schools, hospitals,... and inside battle tanks.

I suppose that places like Varanasi would meet the letter of your description (i.e. "burning of human corpses in the open" and "a place where there are always burnings and corpses and mourning").

I haven't been there -- this English newspaper article (with photographs) says, I don't know how truthfully

But the atmosphere at the giant funeral site is not one of sorrow, as mourners instead laugh, chat and play cards as the funeral preparations are carried out.

...

The closest male relative must perform the funeral rites, while women are traditionally not allowed to be present for fear they will cry and ruin the respectful atmosphere.

But my image of a "charnel ground" would be of abandoned, unburnt, decaying corpses; not a lot of human presence; and maybe carrion-eaters -- like a graveyard except where corpses are not buried nor cremated.

Wikipedia: Charnel ground says

Throughout Ancient India and Medieval India, charnel grounds in the form of open air crematoria were historically often located along rivers and many ancient famous charnel sites are now 'sanitized' pilgrimage sites (Sanskrit: tirtha) and areas of significant domestic income through cultural tourism. However, proper "charnel grounds" can still be found in India, especially near large rivers banks and areas where abandoned people (without family) are cremated or simply left to decompose.

... and cites suttas

'Cemetery contemplations', as described in Mahasatipatthana Sutta (DN: 22) and the Satipaṭṭhāna Sutta (MN: 10):

...have as their objects a corpse one or two or three days old, swollen up, blue-black in colour, full of corruption; a corpse eaten by crows, etc.; a framework of bones; flesh hanging from it, bespattered with blood, held together by the sinews; without flesh and blood, but still held together by the sinews; bones scattered in all direction; bleached and resembling shells; heaped together after the lapse of years; weathered and crumbled to dust.

At the end of each of these contemplations there follows the conclusion: "This body of mine also has this nature, has this destiny, cannot escape it."

Similar are the 10 objects of loathsomeness (asubha q.v.).

Chogyam Trungpa said:

Charnel ground is a symbol of no man's land. It is the ground where birth and death take place; it is prelife and postlife experience. The idea of the charnel ground is that all kinds of experiences coexist simultaneously;

It is a place to die and a place to be born, equally, at the same time -- a wasteland of some kind. The closest thing to a charnel ground in this country is a hospital -- a place where you give birth and a place where death is performed. But the charnel ground is much more than a hospital situation. It is simply our basic raw and rugged nature, the ground where we constantly puke and fall down, constantly make a mess. We are constantly dying, we are constantly giving birth. We are eating on the charnel ground, sh*tt*ng on it, sleeping on it, having nightmares on it. That basic ground which we use all the time is what is known as the charnel ground.

You might feel threatened because the environment is very spooky. You have to give up your arrogance. Giving that up is connected with devotion. Having related with longing and with the absence of arrogance you have to surrender completely. In other words, everything takes place in the charnel ground. It is a place of birth and a place of death.

so as you can see, in Buddhism it's not so much about literal unburied cemetery as it is about naked truth of existence as it is, complete with horrifying and inspiring aspects. Hospital is one place you can experience that naked quality, a country at war could be another, or, if you are really sensitive, you can see the charnel ground aspect in all of our everyday situations.