H1B effective date

From when a person can start working in H1B for the registration done for fiscal year 2022 and got selected in third lottery on H1 approval?

As soon as the petition is approved with change of status and if you are already in the US. Make sure check the start date on the I-797 approval notice.
If you are out of the US, you will need to go for H1B visa stamping.

Thank you! Looks like the petitioning employer filed the petition so after change of status approval by default I go to h1 status or I can continue with my h4 ead just like having multiple h1 transfers we decide which employer to join or not

This depends on the requested start date. Your status will change to H1B on the start date in the I-797 approval notice.