Wireless doorbell systems that have a kinetic-powered button (i.e. no battery) exist, e.g. https://www.amazon.com/gp/product/B0929729L1
Wireless relay receivers also exist, e.g. https://www.amazon.com/gp/product/B0B125VLNB
These products often use the 433 MHz band. Are there any that actually work together? What I really want is a kinetic-powered doorbell button that triggers a relay instead of a chime box.
No technical barrier here. For $10 you can see if it meets your needs