Why did peter the freat wnt to find a warm water port despite the fact that russia already had other posts

A warm water port means your ships can project power year round. The mission of a navy is to protect shipping lanes, or you won't have any economic strength. Projecting power year round lets you protect your own trade by keeping sea lanes open (these are called sea lines of communication, or SLOCs). You protect your trade and your allies. With a navy you can control trade to other countries and mount invasions.