Date icon is different

Anonymous , Once mark a table as Date Table, The Date you chose become id column. This sign for that. This is not more behave like a date. You will also not get a date hierarchy for that.

You can create a new column as per requirement and create a hierarchy on that or have another date column

Refer this link for more definition

Identity field: Fields with this icon are unique fields, set to show all values, even if they have duplicates. For example, your data might have records for two different people named 'Robin Smith', and each will be treated as unique. They won't be summed.

To get the best of the time intelligence function. Make sure you have a date calendar and it has been marked as the date in model view. Also, join it with the date column of your fact/s. Refer :
https://radacad.com/creating-calendar-table-in-power-bi-using-dax-functions
https://www.archerpoint.com/blog/Posts/creating-date-table-power-bi
https://www.sqlbi.com/articles/creating-a-simple-date-table-in-dax/