What is the hotfix applied to your projects? Does the hotfix version applied on admin app matches the version of the Kentico NuGet packages on the live site app? Please, check also the following:
Live site runs on HTTPS (the live site presentation URL uses HTTPS): it looks like your Live site already runs on HTTPS
SameSite mode is configured correctly
Browser does not block 3rd-party cookies
If you are using a self-signed certificate for the live site in the dev environment - you need to accept this certificate in your browser and reload the administration interface