The update_cells call can update multiple cells at once. So you should calculate all new values locally and push the changes in one update. This should use only one token, instead of one per cell (untested code):
def update_sheet(sheet, table, start='A', end='C'):
to_update = []
for i, row in enumerate(table):
cells = sheet.range(f'{start}{i+4}:{end}{i+4}')
for cell, value in zip(cells, row):
cell.value = value
to_update.extend(cells)
sheet.update_cells(to_update)
I also changed the names and indentation to follow Python's official style-guide, PEP8, and used an f-string for easier string formatting.
This still has the problem that it needs to get each row from the sheet, each of which does an API call. Instead you can get each column as a range and update one column at a time, which saves calls if your table has less columns than rows. For this we need to transpose the table first, though:
def update_sheet(sheet, table, columns="ABC", header=4):
to_update = []
table = list(zip(*table)) # transpose the table
for col_name, col in zip(columns, table): # iterating over columns now
r = f"{col_name}{header}:{col_name}{len(col)+header}" # changed range
print(r) # for debugging
cells = sheet.range(r)
for cell, value in zip(cells, col):
cell.value = value
to_update.extend(cells)
sheet.update_cells(to_update)
With this it is no problem to use e.g. this table of size 2500 x 3:
import numpy as np
...
table = list(map(list, np.arange(2500*3).reshape(-1, 3).astype(str)))
update_sheet(sheet, table)