How does this then get resolved? Without a domestic tooling of Putin what other direction does this go in?
It'll get resolved when Putin finally realises he can't defeat Ukraine militarily, can't remove the Ukrainian government, and can't take Kyev.
At that point he will have lost very significant portions of his invasion force and equipment and be left with an utterly demoralised military, withdrawing from some areas of Ukraine but still occupying other areas. And then the real negotiations will begin about what (if any) areas of Ukraine the government is willing to cede to Russia.
Ukraine will not agree to demilitarisation, nor to staying out of the EU. They might agree to not joining NATO.
Putin will then have to decide whether to reject what Ukraine offers, or instead face military conflict without end inside Ukraine. The latter prospect will be a very unattractive option for him, risking substantial further losses with little means of replacing them, and ever-rising unrest inside Russia.