Cannot set vertical datum and other custom parameters for projected CRS data

The UI only supports an EPSG lookup for the CRS name, but oddly enough no EPSG lookup for vertical datum. Why is this the case? Is it possible to use an EPSG lookup for these to prevent user input error? By default, users aren't even aware there is the possibility of a vertical datum to be set since it is hidden in the project shared parameters.

Start by locating the UI handling for the EPSG lookup and the project shared parameters where the vertical datum is currently hidden. Compare how the CRS name is exposed with the available vertical datum and custom projected-CRS parameters. Done means users can access these parameters and use EPSG lookup support to reduce input errors.

Written by the indexing model from the issue text.