This doesn't make to me. They certainly could use a small part of the Fournier TPE to bring in a player, sending out a low salary player creating a small TPE for moving forward, but that does not accomplish all that much. We have other TPE in the hopper we could use.
One thing to keep in mind (that I think is true, no one has correct me in other threads), is that we can take in a contract with the Fournier TPE and so long as we cut the salary down by the end of the season, we avoid the tax. For example, we could take in someone now and trade White at the trade deadline and the tax would be calculated based on the team salary at the end of the season.
I think the Celtics are just keeping all options open. If we could finagle a way to bring in say Ayton and not be hard capped, I am sure they would be open to that (not sure that is possible, just an example).
And the reason that they have not finalized the Brogdon deal may be that they are still discussing Turner or some other variation on the trade. That is very possible. Or there could be physicals involved that aren't going well.