The company I work for will be closed until the quarantine is over. Will this harm the processing of my temporary residence application? Do I have to report it and how?

The answer depends on what "closing the business" means. If the "closing the business" (e.g. stoppage, suspension of business activity) is temporary, for the period of the epidemic, but after its cancelation, the employer will still want to employ you under the conditions indicated in the Annex No 1 to the application for temporary residence and work permit, then you don't have to submit any new documents regarding your case. After receiving your decision granting you a residence and work permit, you will work there.
If, on the other hand, "closing the business" means that your employer, after restoring their business, will not be able to employ you during as declared in Annex No 1, you should inform us in writing about it and indicate the current purpose of your stay in Poland.