Automatic extension when refiling a recharacterization of a Roth IRA to a TIRA?

I have recharacterized a Roth IRA as a TIRA for year 2023. My brokerage may not be able to compute the amount of the transfer in time for april 15 when I need to file taxes. One of their agents told me that the IRS automatically grants an extension when a recharacterization is involved, and that once the amount transferred is known, I would refile.

If that is so, I am unclear on the details.

#1 would I submit my taxes (self employed) as usual and the irs would note the roth recharacterization in the submitted form, and grant the extension?

#2 or so I submit something other than the usual tax forms - something like an extension?

#3 whenever I know the amount that was recharacterized, do I adjust the originally filed tax docs and refile as if it was the first refiling? Or is it an amended tax return?

 

I may not have every file for an extension so I'm unclear on how one submits the final tax return, regarless of the path to get there (file normal by apr 15, or file for an ext).

Thanks