After considering trying to get Sony to fix or replace these out-of-warranty earphones I decided to try to replace the batteries myself. I followed the (excellent) instructions above. After step 5 I could see that the wide ribbon cable had been folded in such a way that it was creased. When I disconnected the narrow ribbon cable the wide ribbon cable snapped at the crease. This was already the end of the device but out of curiosity I opened the other earphone. Its ribbon cable was also creased and also broke under slight tension. This is a serious manufacturing fault.
I am reminded that over the years I have owned other Sony products that developed defects soon after the warranty period, e.g., a CD player that wouldn't play past the middle of the disc.
I have also owned Panasonic products over the years and never had such problems with them, e.g., a VCR from the 90s that works to this day.
Fyck Sony. I have purchased the (Panasonic) Technics EAH-AZ80. They are awesome.