@bschwahn
Thanks for your reply.
The current consumption fluctuates between 50 and 100mA and is due to the Wi-Fi connection (this is what all modules searching for a Wi-Fi connection or exchanging data over Wi-Fi do, so that's not surprising).
I've re-measured all the connections. I haven't desoldered the module yet.
The humidity was approximately 60%. The module was moved between different rooms after the initial firmware update, but before soldering. An ESD issue could have occurred there.
Thank you for your support.