Theoretically, monsoon season extends between Mid-June and September althogh there are some exceptions in it. If you plan to complete trekking in Nepal before the 10th of June, that will be the best idea.
As of today, a foreign traveler need to accommodate for a 7-day quarantine in a hotel although you must have a COVID PCR Negative Report with you before arriving in Nepal. On the Fifth day, you have to retake the COVID-19 PCR test to assure that you are fit for trekking in the Himalayas.
As the Government of Nepal has already provisioned to import COVID-19 vaccines until the end of February, 2021. On this note, the restrictions on tourism may change for spring season.