Should facing bricks be glued to the raw wall or stand free-standing?

Hello,
I have an outdoor staircase with functional (bearing) stringers that are not attractive. There is still space on the foundation, so now a facing wall made of concrete formwork blocks – but nice ones – is to be placed on the left and right. So these hollow blocks that are then filled, a width of 20 cm would fit.
Now the question is whether to bond them to the stringers or let them stand free. If freestanding, there is a gap where water can run in. Can this then be sealed with silicone?
Natural stone steps rest on the stringers, which are flush with the stringers. I would like the walls on the left and right to be a bit higher and have 2 steps.

Usually, it is done the other way around. First the walls on the right and left, and then concrete is poured into a formwork between them. The transition can then be sealed; in the case of free-standing stairs not adjacent to a basement or similar, this is technically not necessary but visually advantageous, otherwise efflorescence may occur.

In your case, it is unfortunately disadvantageous that not only the concrete foundation but also the natural stone covering is already there. Simply using mortar will not keep it permanently waterproof; you will always have water running into the groove between the wall and the stairs. Silicone helps... 2-5 years, then you should scrape it out and renew it at the latest. There are other permanently flexible adhesive sealants that might last a bit longer. It will only be permanently watertight if you lead a seal from the wall from above onto the foundation of the tread step. But there is already a covering on it.

Leaving a gap intentionally will not work, as it will get clogged at the bottom and water will remain there.

Thanks in advance. So it is not a coating, but natural stone steps, which I can take down again. They are not glued yet. They are cantilevered steps. Then I would take down the steps and apply sealing on the rough stringer towards the wall (I have this gray compound that you could smear on with fleece around the corner). Then put the steps back on. They are still loose because they are not all exactly 1 m wide, and I wanted to avoid not being able to lay the steps in the end when the side walls are in place.