The black sediment, if it can be filtered out nearly completely, is most likely fine particles of metallic silver. During development, silver halide mostly from unexposed part of the film can dissolve into the solution, and the silver can be slowly reduced to metallic form. It sometimes happens on the wall of the vessel, or it can make sediment. It sometimes makes mirror surface as well.
If the sediment cannot be effectively filtered out by paper filter, it is most likely sensitizing or antihalation dye that came off the film. Dye molecules are larger than most molecules in the film or developer (except gelatin and other polymers), but they can go through paper filter. However, if allowed to set still, they can aggregate and make more "solid" debris at the bottom of tank. Most people probably observed this in a bottle of film fixers that are reused many times.
Bromide concentration in the developer certainly increases as you process more film in it, but bromide ion is very soluble and it won't make precipitates. It only slows down development, and it also may lose speed.
I'm pretty sure that when Zawadzki, Dickerson and Opitz came up with XTOL-type developers, they hoped that it would be a perfect solution for replenished tank applications, replacing T-MAX RS developers. It is a great pity that a few problems arose since then that prevented widespread use of XTOL for those applications.