When does my second COVID extension in Thailand start if I apply before my first one expires?

>If I go and apply for 2nd extension now, will they add the extension from July 5th,

That'll be up to the immigration office. *MOST* immigration offices sell extension of stays when there are 30 days or less remaining on your existing extension.

The 60 day extension of stay based on unable to travel due to COVID-19 is just that; it's because you can't travel home. However, the immigration offices are giving them out easily. BUT... they *MAY* reject your extension request verbally. It is an optional extension.

Unless you live close to an immigration office, I wouldn't recommend waisting your time to apply for another extension of stay now.