I dont know whether its possible directly from jira but its definitly possible to do it in the database.
You could create a groovy script thats executed in a transition postfunction and thats contact to databases for the current issue and gets the timestampfs of the different transitions and write it in customfield. So you could read it out and get reports of it.
Look at the "Transitions" tab found in the Activity section of an issue (where you can also find comments, issue history, etc.).
You can see the date and time of the last transition, as well as how long it was in the original source status. If there is no data in this tab, then the issue hasn't been transitioned to any other status in the workflow and has always been in its "new" status ever since it was created.
If you want to get this in the Issue Navigator, you're kind of out of luck using default JIRA, unfortunately. You could use an add-on like ScriptRunner to create a scripted field that can display this information for you in a custom field, which you can then place on the Issue Navigator as another column/field.
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