You will get project folders from here

/api/ProjectFolder/GetList

Query String

Parameter	Required	Value
pinProjectId	Mandatory
parentFolderId	Optional
start	Optional	User Input
SortBy	Optional	Name
SortOrder	Optional	0(Ascending) and 1(Descending)
permission	Optional

Request Header

Parameter	Required	Value
TokenKey	Mandatory	User Input
Accept-Language	Optional	en-US
Accept-Encoding	Optional	gzip
Content-Type	Mandatory	application/json
PINProjectID	Optional	User Input

Response

TokenKey → Your-Key

[
  {
    "ProjectFolderID": 132895,
    "FolderName": "Project Specification",
    "ParentFolderID": 0,
    "LevelID": 0,
    "CreatedBy": {
      "PWUserID": 12249,
      "PWAccountID": 12207,
      "PWContactID": 121455,
      "FirstName": "Ayan",
      "MiddleName": "",
      "LastName": "Ghosh",
      "Email": "[email protected]",
      "UserName": "Ayan Ghosh"
    },
    "CreateDate": "2013-07-15T12:54:34.06",
    "ChildFolderCount": 2,
    "DocumentCount": 7,
    "PINProjectID": 12148,
    "PathName": "Project Specification",
    "PathFolderID": ">132895>",
    "Permission": {
      "Read": true,
      "Download": true,
      "Upload": true,
      "Modify": true,
      "Delete": false,
      "CheckOut": false,
      "ChangeTask": false
    }
  }
]

Enum : PermissionSet

Property Name	Description
0 – No	Do not Fetch Permission Set
1 – Yes	Fetch Permission Set

Enum : Permission

Property Name	Description
1 – ReadFolder	Read Folder
2 – DownloadFiles	Download Files
4 – UploadFiles	Upload Files
8 – ChangeFolder	Change Folder

Entity : Project Folder

Property Name	Data Type
ProjectFolderID	Integer
FolderName	String
ParentFolderID	Integer [Nullable]
LevelID	Integer
CreatedBy	User
CreateDate	DateTime
ChildFolderCount	Integer
DocumentCount	Integer
PINProjectID	Integer
ExpiryDate	DateTime [Nullable]
PathName	String
PathFolderID	String
IsNew	Boolean [Nullable]
Permission	Permission
ChildFolders	IEnumerable< ProjectFolder>
ErrorInfo	ErrorInfo

Remarks

Response header parameter Permission will contain folder permission code.
Permission in response body will only come when the value of query string parameter permission is 1 & it holds the permission for logged in user on that folder.
If Read is true then logged in user has permission to View the meta–information of that folder, if Download is true then logged in user has permission to create ShareLink of that folder, if Upload is true then logged in user has permission to Upload file inside the folder, if Modify is true then logged in user has permission to Create sub–folder under that folder, Update folder information and Delete that folder.
Delete, CheckOut and ChangeTask inside Permission in response body is not related to folder permission.