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If you value privacy, ditch Chrome and switch to Firefox now
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This is a most excellent place for technology news and articles.
This is already handled by Firefox's very own Multi-Account Containers extension.
I like to add Sticky Window Containers for extra functionality. Sidebery also works well with containers.
This (and the other suggestions below) are what I've tried previously.
It's close but Google's got the native solution and the "window-level" containers that have individual per-container icons make it much easier for me to sort my sessions. Unfortunately it looks like Firefox still has them relegated to a single taskbar item. I guess this is necessary since container tabs can be moved between windows unlike Chrome which draws a hard line between windows. I guess this is just the method Firefox went with but it makes my processes a lot more difficult.
Thanks for the suggestions. I'll give it another go and check out ungoogled Chromium as well.