What is the correct timing of joining a new company while leaving old one with paid leaves?

I assume I can only join the new company after I have been considered officially quit from the old one. So, if I had 20 days paid leaves left…

+ 30 calendar days notice (equivalent of 20 working days). I'm aware of only 2 weeks notice necessary by law.

– Use 20 days paid leaves

= 1 full month calendar days of rest/not working

I wanted to confirm my understanding whether I could already join the new company during that 1 full month of rest, but I assume no because I am still on the old company's payroll. So I can only join the new company on day 31st, for example.

Please correct my understanding if I'm wrong guys.