How do I seal thin cracks in concrete?

I hope a knowledgeable professional can provide smart tips on materials and method?:

THE PROBLEM:
Thin cracks between the facade and concrete stairs, and the ground (asphalt-sealed concrete slab). If you wash the area with a hose, it starts dripping in the basement directly below after about 5-10 minutes.
The stairs are generally not damaged, so the amount of leaking water is fairly limited, but surface concrete has frost damage from the second step.
The idea is to only repair/apply the asphalt surface layer closest to the meeting between step/facade and facade/ground, where leaks are obvious, and to also seal the second step with an asphalt layer.

I HOPE...
that someone can give a tip on a simple way to, as a precaution, seal thin cracks at depth before patching the concrete damage, (and then brush on new asphalt with fiber cloth reinforcement).

THERE SHOULD be some easily flowing sealing agent that can be simply poured into cracks?! The conditions should be good, as there are wide cracks nearest the surface, where a medium can "fill up" and then seep downwards into the concrete.
(Maybe pure waterglass can be used in this way?)
Perhaps there is "ROCA GIL" for consumer use.
Any knowledgeable "concrete expert" who can give material and method tips?

Check attached image.
 
  • Concrete steps with cracks and damaged mortar, adjacent to a brick wall and a door. Signs of wear and a potential leak site are evident.
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