I chose Turbotax Deluxe $40. When I fill in State Returns (2 states, moved 2020) it says $40 each for these states. Does it mean $120 e-filing? More unexpected fees?

Sorry yes. Deluxe federal is $40.  Then each state is $40.  And if you want to have the fees deducted from a federal refund is another $40 Refund Processing Service charge (45 in California).

Thank You dearly for your fast reply and assistance! Will check other options for filing my taxes