I guess you have a big stamp in your passport from Immigration with the text:
"permitted up to xx Nov 2025"
This stay is permitted based on being employed, if you stop working, you have to cancel this permission to stay as signed at application of this Extension of Stay.
If you have permission from Immigration to make short trips abroad while living on a tourist visa and coming back each and every time to the same address, it is no problem.
If you did not discuss this with your local office, I can not tell you.
Officially you have to report within 24 hours after arrival at the address.
That means when you left Thailand and return or when you decide to stay overnight at another address.
Just for extra info. As you mention that you are allowed to be inside Thailand to study, it may be a problem that you leave twice a month to other countries in stead of sitting in the classroom. Be prepared to answer some questions about the need to travel around.
Which means you stop working, so there is only 1 option.
Get the letter from your employer, visit your local Immigration Office, cancel your Extension of Stay, ending on the same date as last day of employment and apply for a new 1 year Extension of Stay based on visiting Thai family.
And visit the Ministry of Labor to cancel your work permit.
IF
you are in Thailand during the first 90 days you got on entry or at conversion of your stay at local Immigration Office, than you visit your local immigration office and ask IF you can apply for the 1 year Extension of Stay based on visiting Thai family, if not than you need to go abroad to apply for a new visa.
Get the Emergency passport, travel abroad, come back with the Visa Exempt Entry, wait for your new passport and start the visa procedures all over again, starting with new Non Immigrant visa for 90 days and than the 1 year Extension of Stay