I've made an adaptation of your code (in particular, in each iteration I plot only another scatter point, because plotting each time ALL the points soon becomes unbearably slow).

If you will execute this file, as I invite you to do, $ python3 slow.py, it will print 0 50 100 150 200 and, initially fast, then slower and slower, it will produce a progressive display of the data points, all in the same Axes.
I have to confess that I don't understand your problem description because it's so different from what I've seen.
import matplotlib.pyplot as plt
from matplotlib.cm import ScalarMappable
import random
def point():
return (random.randint(0,10), random.randint(0,10))
plt.xlim((-1, 11))
plt.ylim((-1, 11))
random.seed(20221229)
N = 200
cmap = plt.get_cmap('plasma')
plt.colorbar(ScalarMappable(cmap=cmap)).set_ticks((0,1), labels=("1",str(N)))
for i in range(N):
if not(i%50) : print(i)
plt.scatter(*point(), color=cmap(i/N), ec='black', s=80)
plt.pause(0.001)
print(N)
plt.show()