How to display a summary of the user permissions of a data table in a row

In my opinion, the drop-down menu is not a good solution in this case.

How could we present the summary in a cleaner way in which if the user expands the card, the data can still be read in the same order as the summary?

I am not sure that, at the time of the occurrence, p. 4-5 accesses –
The drop-down menu is still a good solution (many combinations)
You can consider submitting Checkboxes

enter the description of the image here
When the system grows, you can enter something like permission inheritance. (that is, the user has the same rights in B as in A)

The way it is organized is that the permissions are grouped in the summary (first row from left to right, second row from left to right, etc.) and from top to bottom in the interactive table. I am not at all convinced that the flow is readable or visually appealing. Does it help to add a pie chart in the summary?

According to the Z principle: in our culture we read from left to right

enter the description of the image here

It may not be possible to group the permissions into separate columns because the types of permissions will be a growing list and the user adds a new row, enters the name of the project and sets the permissions in a row.

If it is not possible to group in the column to make it worthwhile categorizing Y developing a group of users instead of selected rights.

  • User – can read write
  • Administration – can everything
  • Devops – can read, write, display

However, this approach requires a lot of analytical and implementation work.

Custom permissions, reading, writing, implementation, etc. they are listed vertically while the summary shows them horizontally. Is this acceptable? Maybe add a tag in each row to make it clear that permissions are sorted automatically? Or add tags and separate "add row" by permission type?

Yes, multi-selection, when labels are displayed horizontally it is acceptable as in the image below.
enter the description of the image here

Does automatic classification work in this case? The way I imagine it would work from this design is when a user sets the permission for a project in a new row, that row will be automatically organized with the same type of permission. Like Gmail, alphabetically order tags after entry.

Possible, but difficult to implement: in this case, you can filter with permission.
It is useful to limit the possible rights at this stage (to start the tests). The programming solution should be generic in this case.