Can I change the battery of the keyboard?

Yes, the battery can be changed.

For out-of-warranty devices, you can acquire the replacement battery on the partner(s) site below, which also provides a comprehensive repair guide. Availability varies by country/region and is subject to changes. Please visit the partner(s) website to confirm if the battery can be shipped to your country. Visit logi.com/support/slimsolarplus for more details.

Partner(s) website(s):
iFixit - www.ifixit.com/Device/Logitech_Signature_Slim_Solar_Plus