Instagram detection

What's the best approach for managing cookies across multiple accounts to avoid detection?

You can use antidetect browser, they allow you to import cookies to created profiles. Antidetect browser will help you change your browser fingerprint by create differnt profiles with different sets of browser fingerprint so websites can't detect you are using multiple accounts. Some recommendations are hidemyacc. multilogin, gologin, dolphin, ...

Try free trial to test about those antidetect browsers like MoreLogin and combined with proxy service like lunaproxy, in order to see whether ur cookie are detected. Normally longer cookie farming will help u with ur accs farm.