I don't think winter transfers are generally more expensive because there is usually less competition from other clubs. During summer transfer windows all the clubs are checking their inventory thoroughly and make plans. Sometime you are right though and I think it is not so much the player problem who could be asking for more salary, but the club who has to let him go knows that the interested club has an emergency and a gap to fill most likely in the fastest possible way. It's not surprising then if they add millions to the initial price tag.
Osimhen now has to consider thoroughly whether Manchester United is still a possible destination for him as they most likely don't play any big competition next season unless they win the Europa League.
Yes the winter transfer window doesn’t necessarily mean it is expensive to sign players but one that I can say makes it hard to get player during this period is the importance of such players to their team, if a player is the bedrock of the team then it is difficult to actually get him away from the team and the one way to lure them away is actually through having to pay huge amount of money to entice his club or if the player’s contract is expiring and he doesn’t want to register.
As for case of Osimhen it wouldn’t have cost Manchester United extra aside his release clause then because it was in his contract on loan at Galatasaray that he can leave at any time. So even if Manchester United goes back to Osimhen it will still be heavily dependent on if they can be able to pay the Release clause and his wages and if this requirements are met I don’t see Osimhen rejecting Manchester United just because they don’t play European competitions, the only club that can change his heart away from Manchester United will be Chelsea because of Drogba his idol