Add an icon for unread message on project task. Otherwise can’t tell which task was updated with a new message without checking inbox.
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It’s an interesting idea , though I personally think that mixing what Inbox does with what the Task List does might be a risky/confusing game, but just my personal opinion.
You can consider instead activating the metadata field to get an overview of when the task was last modified by activating the “Last Modified On” - check out this post by @Rashad_Issa for more info