Hanging attachment - planting stones or car tires?

Such a slope modeling will never be cheap. First, clarify whether it is even permissible. Then you can discuss solutions. Depending on the rest of the situation (extended slope or just filled land), it may also be possible to work only with gravel and geogrid.

The height and steepness may require a professional to plan it and get it approved if necessary...

Car tires? Really? I'm not sure if you will get approval for a special landfill in a residential area.

...
They contain toxic substances that must not be released into the environment.

Which ones?

Which ones?

Manageable PAK, plus zinc and sulfur. But overall nothing severe or that would suggest soil contamination.

Approximately 10% of the tire consists of chemical additives such as plasticizers, vulcanizing agents, zinc oxide, utadiene, thiuram, PAK, 1-Octanthiol,

The shoulder material is examined for pollutants, among other things because of tire abrasion, and must be disposed of if necessary.

For a wall like this, quite a lot adds up. Maybe limits are adhered to today, but what about in 3 or 4 years? Where is the boundary between upcycling (use as a planter ring) and illegal dumping?

As long as there is no abrasion, I see only a low risk that water will cause dissolution or leaching. When there are small children in the house, I see it as somewhat more critical, since they also want to touch and lick everything. For this reason, there are increased warnings against making toys for children from used car tires. Overall, I would not want used tires in the garden either.

But that is not necessarily the topic here ... :)