Example how to display images drawn with Cairo in Pygame.

pygame_cairo.py

import cairo
import pygame
import sys

SIZE = (400, 400)

def draw_frame(cairo_context, position):
    cairo_context.set_source_rgb(1, 0, 0)
    cairo_context.rectangle(position, position, 10, 10)
    cairo_context.fill()

def loop():
    pygame.init()
    screen = pygame.display.set_mode(SIZE)
    clock = pygame.time.Clock()
    position = 0
    while True:
        for event in pygame.event.get():
            if event.type == pygame.QUIT:
                sys.exit(0)
        cairo_surface = cairo.ImageSurface(cairo.FORMAT_ARGB32, *SIZE)
        draw_frame(cairo.Context(cairo_surface), position)
        screen.fill("black")
        screen.blit(
            pygame.image.frombuffer(cairo_surface.get_data(), SIZE, "BGRA"),
            (0, 0)
        )
        pygame.display.flip()
        clock.tick(60)
        position = (position + 1) % (SIZE[0]-10)

if __name__ == "__main__":
    loop()

$ python
Python 3.9.10 (main, Jan 17 2022, 00:00:00) 
[GCC 11.2.1 20210728 (Red Hat 11.2.1-1)] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import pygame
pygame 2.3.0 (SDL 2.24.2, Python 3.9.10)
Hello from the pygame community. https://www.pygame.org/contribute.html
>>> import cairo
>>> cairo.version
'1.20.1'