Как сделать для каждой вкладке свой textEdit?

Вам надо создать свой класс для виджета, например class Widget(QtWidgets.QWidget):. Заполнить его чем вам надо и все.

import sys
#import os
from PyQt5 import QtWidgets, QtCore, QtGui
from PyQt5.QtCore import Qt
from PyQt5.QtWidgets import QFileDialog, QMessageBox

#import MainWindow
class Ui_MainWindow(object):
    def setupUi(self, MainWindow):
        MainWindow.setObjectName("MainWindow")
        MainWindow.resize(381, 265)
        self.centralwidget = QtWidgets.QWidget(MainWindow)
        self.centralwidget.setObjectName("centralwidget")
        self.tabWidget = QtWidgets.QTabWidget(self.centralwidget)
        self.tabWidget.setGeometry(QtCore.QRect(10, 10, 361, 201))
        self.tabWidget.setObjectName("tabWidget")
        MainWindow.setCentralWidget(self.centralwidget)
        self.statusbar = QtWidgets.QStatusBar(MainWindow)
        self.statusbar.setObjectName("statusbar")
        MainWindow.setStatusBar(self.statusbar)
        self.menubar = QtWidgets.QMenuBar(MainWindow)
        self.menubar.setGeometry(QtCore.QRect(0, 0, 381, 21))
        self.menubar.setObjectName("menubar")
        self.menu = QtWidgets.QMenu(self.menubar)
        self.menu.setObjectName("menu")
        MainWindow.setMenuBar(self.menubar)
        self.action = QtWidgets.QAction(MainWindow)
        self.action.setObjectName("action")
        self.action_2 = QtWidgets.QAction(MainWindow)
        self.action_2.setObjectName("action_2")
        self.menu.addAction(self.action)
        self.menu.addAction(self.action_2)
        self.menubar.addAction(self.menu.menuAction())

        self.retranslateUi(MainWindow)
        self.tabWidget.setCurrentIndex(0)
        QtCore.QMetaObject.connectSlotsByName(MainWindow)

    def retranslateUi(self, MainWindow):
        _translate = QtCore.QCoreApplication.translate
        MainWindow.setWindowTitle(_translate("MainWindow", "MainWindow"))
        self.menu.setTitle(_translate("MainWindow", "Файл"))
        self.action.setText(_translate("MainWindow", "Сохранить"))
        self.action_2.setText(_translate("MainWindow", "Новый файл"))


class Widget(QtWidgets.QWidget):                             
    def __init__(self, val):
        super().__init__()
        self.textEdit = QtWidgets.QTextEdit(f'{val}'*10, self)
        v_layout = QtWidgets.QVBoxLayout(self) 
        v_layout.addWidget(self.textEdit)            

#class App(MainWindow.Ui_MainWindow, QtWidgets.QMainWindow):
class App(QtWidgets.QMainWindow, Ui_MainWindow):
    def __init__(self):
        super().__init__()
        self.setupUi(self)
        self.tabWidget.setTabsClosable(True)
        self.tabWidget.tabCloseRequested.connect(self.close_tab)
        self.action_2.triggered.connect(self.create_file)
        self.val = 0

    def create_file(self):
        self.tab = Widget(self.val)               # QtWidgets.QWidget()     # !!!
        self.tab.setObjectName("tab")
        self.tabWidget.addTab(self.tab, "")
        str = f"NEW {self.val}"
        self.tabWidget.setTabText(self.tabWidget.indexOf(self.tab), str)
        self.val += 1

    def close_tab(self, ind):
        self.tabWidget.removeTab(ind)


def main():
    app = QtWidgets.QApplication(sys.argv)
    window = App()
    window.show()
    sys.exit(app.exec_())


if __name__ == '__main__':
    main()