Rumor has it that Russia is pushing hard because Putin has to announce his candidacy for the March 2024 presidential election soon, and he wants a victory he can include when he announces that.
This may also explain why Russia keeps pushing, apparently disregarding very bad weather for it, they have tried to attack through mud, which you won't believe how bad it is, unless you've seen it, and they also tried to attack through the recent blizzards!
This is the reason Russian losses are way higher even than when they took Bakhmut.
But there is no way from what I've heard, that Russia can take Avdiivka quickly, it's way better defended than Bakhmut, so Russian losses will probably remain high as long as they keep trying. This city has actually been a target for Russia since 2014 AFAIK, and it's heavily fortified and defended.
My guess is that when Russia fails to take it before the Speech, Putin will move the goal post, and want to take it before the election. So this could continue through the winter, at extreme cost to Russia, because Putin is actually not a clever strategist, he is just ruthless, stubborn and scared, with a major inferiority complex.