You did not show the code that receives the file path from the file chooser and puts it into the TEdit, or show what the file path actually looks like. But ACTION_GET_CONTENT is documented as returning a "content:" uri, which requires you to use the ContentResolver class to access the file data.
But TIdMultipartFormDataStream.AddFile() uses TFileStream, which wants direct access to the file, which will not work with a "content:" uri on modern Android versions.
So you will likely have to either:
access the file yourself via Android APIs and read its byte data into a TMemoryStream or TByteStream, or
create a custom TStream that wraps an Android InputStream from the ContentResolver.openInputStream() method
And then use TIdMultipartFormDataStream.AddFormField() instead of TIdMultipartFormDataStream.AddFile() to send whichever TStream you end up using.
Alternatively, you can use ContentResolver to extract the underlying "file:" uri from a "content:" uri, and then you should be able to open the file using a normal TFileStream (provided you have permissions to the file).
Also, when using ACTION_GET_CONTENT, the ACTION_GET_CONTENT documentation says to wrap your Intent with Intent.createChooser(), and also include CATEGORY_OPENABLE and FLAG_GRANT_READ_URI_PERMISSION on your Intent.