I have just installed the macOS Catalina 10.15.5 update on my 11" Mid 2013 MacBook Air. The update is working fine.
The MacBook Air specifications on the Wikipedia page says that this model has a lithium-ion battery, 'tho I haven't unscrewed the case to look. But the new Battery Health controls in System Preferences → Energy Saver don't appear.
Not a lithium-ion battery? Or perhaps other differences in this model prevent Battery Health from showing up? Something else?