Main problem of showing progress bar in Blender UI is that while a script is running the UI is frozen. So the simplest (?) solution is to break execution whenever the progress status should be updated. For this you can use either timers or modal operators. The last one can't be switched on during all time of Blender execution and has some starting costs.
import bpy
from functools import partial
def show_progress(area):
if show_progress.iteration >= 100:
area.header_text_set(None)
return
else:
area.header_text_set(f'Loading {show_progress.iteration}%')
show_progress.iteration += 0.5
return 0.01
show_progress.iteration = 0
bpy.app.timers.register(partial(show_progress, bpy.context.area))
Novice question: how would one feed the text to be shown to such function, from inside an operator class? I have an add-on that loops through a lengthy list, and I'm trying to apply this but I'm not getting anywhere (it must be something obvious, but…).