I received a separate request letter from IRCC asking for the CSQ + other additional documents.
However, my sponsor eligibility letter did state the following:
Provincial Requirements for Residents of Quebec
If you are a resident of the province of Québec, you must submit an undertaking application to the Provincial Government.
To download the required forms, please consult the Ministère de l’Immigration, de la Francisation et de l’Intégration (MIFI) website at
www.immigrationquebec.gouv.qc.ca (Sponsors and Sponsored Persons section).
Complete the required forms and promptly submit them to the MIFI at the address provided in the provincial guide. Do not submit any of the MIFI forms to this office as they will only be returned to you. You must enclose a copy of this correspondence with your undertaking application to MIFI. If you received this communication via email, you may print a copy to be enclosed with your undertaking application to MIFI.
I think if you already received this sponsor eligibility letter you should be good to proceed with CSQ once Quebec restarts accepting undertaking applications in June.