Pin Live chat or certain labels to top of inbox

Business problem

My Customer support team sometimes misses live chat escalations during busy periods of the day. Since these descend to the bottom of the inbox when new tickets flood in.

Wished result

I would like to have the option to pin live chat requests always to the top of the inbox. or have the ability to pin tickets with certain labels to the top aswell. Kind of like a high priority functionality.

Even though the live chat requests already get a golden border, this sometimes still isn't enough for our support team. and we strive to answer live chats within 5 minutes.