Air Asiana canceled return flight while on a trip. How to get most compensation (and a flight)

A while ago I bought a flight+return from Japan to Korea. Now I am in Korea (used the first flight) and have just received an email that my return flight has been canceled (a couple weeks ahead). The email looks legit (correct sending email server, reservation number, flight number etc.). The email is also very short and otherwise not informative, telling me to contact the point of purchase, which is their own website.

Due to work and visa requirements, I need to buy a new ticket for the same date and fly to another city in Japan. This will incur major cost for me, as I will not be able to quarantine at home or reach home without public transport for reasonable cost. I would have to buy a 300km taxi ride home or stay is some quarantine hotel for some days if I do not fly directly to my home city.

Is there a way to make Air Asiana pay for this cost? After all they sold me a ticket and I already paid for it. Now they want to unilaterally change the contract and leave me with major cost. Can I make them fly me to a different city and pay for the quarantine hotel cost and inner Japan travel or a long distance taxi ride home?

EDIT
I tried calling customer support (waiting for about 10 minutes), but they only have Korean speaking staff available today. Need to call another day and wait again. Simply rebooking online on their website also did not work. Cannot find a suitable category. First impression customer service: Very bad.

EDIT2
As promised, I would keep this updated. So I called again. Waiting 20 minutes to get through :-( Once I got somebody, they just told me I could fly on a different date, to a different city, or get a refund. For a different date, they were not sure when another flight would be available. Other cities in Japan are at least 300 km away, and they did not offer a domestic flight or train to transport me to my destination. Now, for the refund, they could not even tell me how much that would be. They don't have qualified staff there at the moment and due to Korean New Year holidays coming up, I would have to call again on Thursday. Talk about customer service, for something which Air Asiana screwed up!

EDIT 3
Final call at the company today (hopefully, had to wait 30 minutes before someone picked up). They flat out refuse to fly me to any city in Japan and then to my destination (which I have bought and paid a ticket for). They also refuse to pay for train transportation in Japan. They also refuse to put me on a different flight on my purchased route, though I admit that I did not find any company currently offering that route. So I took the refund option and will fly to a different city (and with a different company, of coure) and organize travel inside Japan by myself, even though this may be complicated due to quarantine restrictions :-(. At least it is a bit cheaper then just accepting the rebooking offer to a different city. What really upsets me is if I would have known that Air Asiana simply cancels my return flight, then I would have chosen a different airline to begin with. That would have been cheaper then the situation now. Another thing which upsets me is that they said they will refund me in a month. Why? It is my money, please hurry up.

LAST EDIT
Got my money back from the airline, after just about 10 days. Faster than expected, but still a very unpleasant experience dealing with that company.