I have now done some research and found a solution: Logitech has apparently built a tragic design flaw into at least the first batches of Spotlights: When their battery is discharged, there is no power to operate the charging logic, even if the device is plugged into the charger... This means that in such a case, the darker plastic piece at the back (labelled "logi" in large letters) must be carefully loosened with a Japanese knife (it is glued on and snaps into place at the top) and pulled away downwards. Then use a Japanese knife to scrape off the yellow film at the battery connections. I then charged the LiPo battery for 1 minute using a 9V battery and a small cage (https://www.digitec.ch/de/s1/product/max-hauri-9v-block-batteriehalter-2-stk-batterie-zubehoer-12456347) (black=minus pole, red=plus pole). Lo and behold. Then the Spotlight worked like new again. Cover back and that's it. Now I have to make sure that it no longer discharges deeply.
Unbelievable that the USB-C voltage in their design can't be used for this. I hope Logitech has changed this in the newer batches. A clear design flaw.

Now it's clear why the device no longer works. I don't need it for presentations every year, but now it's already rubbish!

The deep discharge of lithium or alkaline batteries has nothing to do with Logitech. Deep discharge cannot be fixed, it is due to the battery cell technology. You should know that all rechargeable batteries that are stored for a long time should be trickle-charged at least once a year (approx. 60-80%). This applies to all batteries! I used my Spotlight again yesterday. Battery was charged after the last

use about 1 year ago. Plugged it into the notebook, started the software and lo and behold, the battery was only half full. Incidentally, the batteries from the DJI Mavic Pro drone are the worst. They're empty after 12 months of storage, and after 24 months they're probably gone. Sorry, but it's an experience you have to make.

The deep discharge of lithium or alkaline batteries has nothing to do with Logitech. Deep discharge cannot be fixed, this is due to the battery cell technology. You should know that all rechargeable batteries that are stored for a long time should be trickle-charged at least once a year (approx. 60-80%). This applies to all batteries! I used my Spotlight again yesterday. Battery was charged after last use about 1 year ago. Plugged it into the notebook, started the software and lo and behold, the battery was only half full. Incidentally, the batteries from the DJI Mavic Pro drone are the worst. They're empty after 12 months of storage, and after 24 months they're probably gone. Sorry, but it's an experience you have to make.