OK, so this isn't a question about the real world. this is a research question for a World building Project
Think of it like a though experiment.

So the Environment in which these bacteria live is very polluted. there's a massive range of volcano's that's spreading a thick oily Ash everywhere. creating a massive continent wide Desert of the Stuff.

This Ash Pollutes Rainclouds, causing them to Precipitate a Inky Black Rain called "Inkfall" this rain stains the ground for a bit.

this Soot and Ash Polluted Water (Called an "Inkwell" by natives_, is Toxic to most things. it's high in sulfur and carbon. but it also contains vital nutrients in very large amounts.

An Algae Lives on the Surface of this water, it takes in sunlight and Nutrients from the environment, and Purifies the water slowly through osmosis, leaving the more toxic stuff and an oily black pigment behind that dissolves back into the water.

over time the toxic Chemicals in the water kill most of the Algae off, and the population of another bacteria that thrives on the toxic chemicals. (I haven't decided on a name for these yet. bare with me) these bacteria absorb the Toxic Stuff and change it into nutrients and such. then they mostly die off when the toxic chemicals in the water are used up. this puts vital Nutrients back into the water which allows the algae to grow again. and so on,

My problem is how the bacteria Survive without sunlight. since they live under the water. which is a very dark black. like ink.

the water is very hot due to the Environment.

also over time, as both organism, evaporation leave a black oily pigment Behind, the water slowly turns into a form of Naturally occurring ink,

That's the basic gist. is there any bacteria or algae that live in heavily polluted environments like this one? how do they survive, and how do some bacteria survive without sunlight?