To be clear i don't think Scheierman and Hauser are exactly the same player type. Sam is almost exclusively an off ball guy, Shceiermna has more on ball skill. Hauser is a bit bigger, more of a 3/4 while Scheierman is a 2/3.
I don't think Scheierman means much for Hauser this year. The C's when healthy have a solid top 8 in their starters +Al/Sam/PP. But regular season rotations are routinely more than eight guys, and KP is not going to be healthy to start the year which will open up some wings minutes as the C's will likely play some amount of KP's time smaller. So I coudl easily see Scheierman as the 9th man with regular rotation minutes at least in the regular seaosn.
What gets interesting is 25-26. The C's will and should be trying to extend Hauser, but that doesn't mean he'll still be on the team in 25-26. The C's will be 25+ million into the luxury tax in 25-26 even without Horford or Hauser on the team, and they'll be in the repeater tax. That means a GIGANTIC tax bill. If you can replace Hauser, making lets say 13-15 million, with Scheierman making less than 3 you could save literally 100 million in luxury tax.
Even if you don't care about ownership's tax bill, and you shouldn't, signing Hauser at least gives you a mid-level contract you can flip in order to bring in a big man to replace Horford if he decides to retire. Having a back-up plan for Hauser makes that a lot easier to do.
To me the C's should be aiming to get Hauser on a MLE deal, that way he's tradeable into another teams MLE into the future (the new CBA lets you use the MLE as a trade exception). If the decline his option (6/29 decision date), that would be a pretty good indication they have a deal worked out, but picking up the option doesn't mean they won't extend him. It just depends on how they want to structure his money.