Answer
Aurena access works on a fundamentally different model from IEE's presentation-object/database-object grants — Aurena screens are backed by projections, and a user needs the relevant projection granted to a permission set they hold, separately from whatever IEE-side access they already have. To find out which specific projection a given Aurena page depends on, enable the debug console while on that page (this surfaces the projection name being used), then go to the Projection Summary page, search for that projection, and grant it to a permission set already assigned to the user.