Celtics2021 is all over this as usual, and I am seeing about the same with my spreadsheet, $15M'ish to stay under the tax and $23M'ish to stay under the 1st apron. There is some variability due to Team Option contracts and contracts for draft picks, but these are the approximate ranges.
But BOS is still over the salary cap so they can't just sign players. The can sign their own (such Vucevic) without many restrictions, but if they sign someone not previously on BOS, they have to use the MLE (about $15M, coincidentally), or the BAE (about $5M). So the options exist, but there are limitations.
They could dump Hauser's contract and free up an additional $10M, but it would be hard to use all of that just through FA signings. In a trade, Hauser can go out and the TPE can be used on a player coming in, allowing BOS to take in a larger salary up to $27M.