Let define the container icon with all the emojis. So there should be no more problems that there is no icon for a situation
This likely isn't going to happen as not all platforms support emoji's natively and part of the reason we use the icons is so you can see the tab highlight colour also.
To my knowledge, all platforms with proper Unicode support can display emoji in it's colorless mode. That could be taken advantage of in order to color the same emoji with different Container colors.
See also my similar (unfortunately closed) request: #984
What platforms don't support Unicode these days? If that's a problem, there can be a fallback for them, but otherwise it should be fine to use any Unicode symbol there really.
I also find the current set of icons very limiting.
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To my knowledge, all platforms with proper Unicode support can display emoji in it's colorless mode. That could be taken advantage of in order to color the same emoji with different Container colors.
See also my similar (unfortunately closed) request: #984