NavMesh

Can you please tell me, is it possible to correct the navmesh manually or draw as it was in the Skyrim editor?

It is a pity that it is impossible by hand.

But what if you attach a raycast NPC, and relying on collisions with colliders, it will walk? Do you know if there are ready-made solutions?

Give it a try! There are other navigation solutions, both free and for sale on the asset store.