M Turner has zero trade value. I doubt CLE would trade both Allen and Mobley. This would be a huge devalue down low for the CAVS trading for Turner. They would not win a title with this trade and would be demonstratively worse.
If that's true, then the Celtics should trade him into our TPE for nothing.
He was the starting center and a core contributor on a finals team that went toe-to-toe (by himself) with Holgrem and Hartenstein.
He can be underwhelming sometimes, but there is no denying that he can be a contributor to a playoff team.
Then the question becomes is he worth getting back into the tax for, because trading him into our TPE still adds to our salary cap - and eventually having to cost our (estimated) $50m worth of extensions for PP, Baylor, Garza, Queta and Walsh in 2027-28 an extra $40m in tax (from $120m to $160m) because we didn't get to reset our repeater rate. I know, it's only money, once you start talking in millions it loses its meaning 
If we offload Hauser, then you can do both. I'm not a big Turner fan, but acknowledge that he does fill a need and does have valuable deep playoff experience.
Right now with all of 14 of our roster spots accounted for, we have around $13M in cap space. If you remove Shulga, that is $15M, but then you immediately replace him with Turner (26.5M), and that is $11.5M over. Hauser makes $11M next year, so it's as easy as trading one minimum at the deadline, and then filling that spot with a prorated player. Banton has a hold at $2.8M - even easier in that case.
This isn't accounting for any possible Jaylen or White trade and it's not my preference, but it is doable to get under the tax and acquire Turner if we're willing to sacrifice Hauser. No MLE at this point either