This is Nonsense and it's not true even if they told you that over the phone.
Based on the government website which they update monthly number of PR granted these are the numbers for this year for Quebec Skilled worker (PEQ, REG) :
JAN: 1585
FEB: 1365
MAR: 960
APR: 120
MAY: 350
JUNE: 435
Obviously they're not working in full capacity BUT FOR SURE THEY ARE OPERATING.
AND These numbers are for all the immigration programs in Quebec which they grant PR:
JAN: 3195
FEB: 2810
MAR: 1960
APR: 195
MAY: 1425
JUNE: 1365
How they prioritize the applications is unknown but they're working even during the peak of pandemic.
Source:
https://open.canada.ca/data/en/dataset/f7e5498e-0ad8-4417-85c9-9b8aff9b9eda