I was intending to write some posts on a bit of the same topic, but never got to it.
There is no official policy on free transportation for Ukrainians in Norway as such. In general, refugees doesn't get free transport - but like in Oslo, there is free transport for Ukrainians now, on all transport except the trains. The train company offers one trip for Ukrainians that has just arrived to the country and need transportation to the place they are going to stay at.
The free transport offer won't last forever - and I think it shouldn't - refugees are supposed to integrate and get a job - but it's very difficult when it takes ages before the bureaucracy can produce a simple work permit, and when it's almost impossible to navigate through the job offerings without any knowledge of the English language.
RE: Benefits are slowly being cut off for the Ukrainian refugees - Netherlands