Start again button"

I want to implement a "play again" button in a game (made with pygame). To do this, I decided that I could use a "loop within a loop". The first cycle is used to make the start button of the game, the second - the main cycle, and starts at the end of the second, i.e. when the player loses. After the start of the 3rd cycle, the "play again" button should appear, after clicking on which, according to my idea, the 2nd cycle should start again, but this does not happen.

run = False
start = True

while start == True:
   window.fill((0, 0, 0))

   # draw btn
   window.blit(start_btn, (0, 0))

   # draw borders
   pygame.draw.rect(window, (255, 248, 220), [245, 35, 5, 810])
   pygame.draw.rect(window, (255, 248, 220), [245, 35, 800, 5])
   pygame.draw.rect(window, (255, 248, 220), [245, 840, 800, 5])
   pygame.draw.rect(window, (255, 248, 220), [1045, 35, 5, 810])

   # get cursor position for click
   pos = pygame.mouse.get_pos()
   x = pos[0]
   y = pos[1]

   for event in pygame.event.get():
      if event.type == pygame.QUIT:
         sys.exit(0)
      
      if event.type == pygame.MOUSEBUTTONUP and event.button == 1:
         if x > 500 and x < 800 and y > 295 and y < 580:
            run = True
            
   pygame.display.flip()

   # main cycle
   while run:
      # fill screen with black color
      window.fill((0,0,0))

      # draw a part of snake
      for x, y in snake:
         pygame.draw.rect(window, (124, 252, 0), (x, y, snake_size_x, snake_size_y))

      # draw food img
      window.blit(egg_img, (egg_spawn_x, egg_spawn_y))


      # draw borders
      pygame.draw.rect(window, (255, 248, 220), [245, 35, 5, 810])
      pygame.draw.rect(window, (255, 248, 220), [245, 35, 800, 5])
      pygame.draw.rect(window, (255, 248, 220), [245, 840, 800, 5])
      pygame.draw.rect(window, (255, 248, 220), [1045, 35, 5, 810])

      # EXIT from game
      for event in pygame.event.get():
         if event.type == pygame.QUIT:
            run = False
            start = False

      # fps
      fps.tick(10)

      # control movement
      keys = pygame.key.get_pressed()

      if keys[pygame.K_w]:
         dir_x, dir_y = 0, -1
      if keys[pygame.K_a]:
         dir_x, dir_y = -1, 0
      if keys[pygame.K_s]:
         dir_x, dir_y = 0, 1
      if keys[pygame.K_d]:
         dir_x, dir_y = 1, 0

      snake_x += snake_speed * dir_x
      snake_y += snake_speed * dir_y

      # we append every move to snake-list
      snake.append((snake_x, snake_y))
      snake = snake[-lenth_snake:]


      # What we are doing if food is eaten
      if snake_x == egg_spawn_x and snake_y == egg_spawn_y:
         # spawn new egg
         egg_spawn_x = random.randrange(370, 851, 40)
         egg_spawn_y = random.randrange(160, 641, 40)
         window.blit(egg_img, (egg_spawn_x,egg_spawn_y))

         # update snake-lenth
         lenth_snake += 1

   
      # What we are doing if we have collision
      if snake_x > 1050 or snake_x < 210 or snake_y > 840 or snake_y < 0:
         # run = False
         # start = False
         finish = True


         while finish:
            window.fill((0, 0, 0))

            # draw btn
            window.blit(gameOver_btn, (0, 0))

            # draw borders
            pygame.draw.rect(window, (255, 248, 220), [245, 35, 5, 810])
            pygame.draw.rect(window, (255, 248, 220), [245, 35, 800, 5])
            pygame.draw.rect(window, (255, 248, 220), [245, 840, 800, 5])
            pygame.draw.rect(window, (255, 248, 220), [1045, 35, 5, 810])

            # get cursor position for click
            pos = pygame.mouse.get_pos()
            x = pos[0]
            y = pos[1]

            for event in pygame.event.get():
               if event.type == pygame.QUIT:
                  run = False
                  start = False
                  finish = False

               if event.type == pygame.MOUSEBUTTONDOWN and event.button == 1:
                  if x > 565 and x < 740 and y > 420 and y < 595:
                     points = 0
                     finish = False
                     
               # save all
               pygame.display.flip()

      # save all
      pygame.display.flip()

pygame.quit()