I think the default will be to favor Lewis. Not in a malicious way, but rather just because that's been the (earned) habit of the last few years and they probably expect him to come out on top anyway.
But within the first few races, if Russell looks immediately competitive, I doubt they would hold him back and they will start to pay more attention to him. Bottom line is I think it's entirely up to Russell how this plays out. If he proves unable to challenge, then he'll get as much support as Bottas did. If he lays down the gauntlet to Lewis from the beginning, he'll effectively force then to take him seriously. I think it's always been like that