Lightning protection external chimney stainless steel experiences

A friendly hello to everyone,

for our individually planned and soon to be built single-family house in timber frame construction without a planned lightning protection system, the question now arises whether an external chimney made of stainless steel needs to be grounded.
The specialist company installing the chimney said they have not done this anywhere for many years, but the electrician and the foundation company have a different opinion.
Since the chimney outlet is the highest point of the building, the likelihood of a lightning strike would also be highest here. Could it therefore make sense to ground it, even if the house otherwise has no lightning protection system?

Thank you very much for your assessments,
Best regards

To my knowledge, the chimney must be integrated into the potential equalization according to VDE. But don’t ask me now where it says that. I already had the discussion a few years ago with the chimney sweep/electrician and they showed me the passages.

I searched briefly. Maybe this from 2018 will help you further - it is a publication by BDH and VDE