Celsea should be challenging for the title next season and that's how they can get back the honor of the club. Chelsea isn't known for how they ended last season, they're known for winning. We aren't over expecting them to win the race but they should be in the conversation and be challenging other top clubs.
I don't think Chelsea will be competing for the EPL title next season, they have a lot of ground to cover before they can challenge for the EPL title again, they have a new manager, too many new players that are yet to adapt, and a 'new' hierarchy at the club that's yet to understand how football works (i consider Todd Boehly to be clueless about the beautiful game). Thus, next season Chelsea will be in the race for a top four finish, and if they can add one of the domestic cups to it (either the FA Cup or Carabao cup), then it would be a good first season for Pochettino.
So for next season I don't think Chelsea will establish themselves as competitors in the race for the EPL Trophy. But in the next season it is likely that Chelsea will target the top 4 as their target until the end of the season. Well, like a team that is being rebuilt due to a slump in the last season, it certainly takes time to be able to compete in the title race.
For that, I think Pochettino will maximize the best possible opportunities next season to be able to bring Chelsea to a better ranking and if that works they will have a wiser season in the coming seasons to enter in the hunt for the title. For Chelsea they have made a lot of sales in this transfer window and they will likely need time to establish themselves as a more consistent team and the strongest in the EPL.
I expect to see Pochettino help Chelsea to be on top of the table but that's not going to be easy for them in their current situation that's why we should wait and see how Pochettino is going to rebuild this team because the Chelsea we see right now is completely broken and this will take some time for Pochettino to do some reworks with his team and make them have better performance than we saw in the last season.