I am having the exact same problem. Here is a simple example of what is getting 503 error:

import pandas as pd
from google.cloud import bigquery

# Sample DataFrame
x = [1, 2, 3, 4, 5]
y = [123, 345, 456, 678, 234]
df = pd.DataFrame({'x': x, 'y': y})

# Construct a BigQuery client
client = bigquery.Client()

# Define table reference
table_ref = client.dataset("TESTING").table("TEST")

# Load data into BigQuery
job = client.load_table_from_dataframe(df, table_ref)
job.result()  # Wait for the job to complete

If you have found the solution to this, please share with me.