Yes, if the Extension of Stay expires while you are abroad, you have to start from the beginning with a new Non Immigrant O visa based on marriage and later for a new Extension of Stay.
There is no Covid Visa, there is an Extension of Stay based on being unable to travel due to Covid. Just to mention it.
If you entered Thailand using a Tourist Visa and are stil in the first 60 days of your Admitted to Stay period, you must first apply for the usual 30 day Extension of Stay based on Tourism.
I guess you have an Extension of Stay based on being married with a Thai National.
You have to visit the Immigration Office to transfer the stamps into your new passport, you need the letter from your Embassy if you applied for the new passport inside Thailand. As you are in the Immigration Office to transfer the stamp, you can ask if the update of the address registration is needed.
The 30 Day Visa Exempt Entry can be extended ONCE with another 30 day based on tourism. You can do this on the 3rd floor of IT square Laksi Plaza Cheangwattana road in Bangkok.
After your visit to the Ministry of Labor to cancel YOUR work permit, you walk into the Immigration Office to cancel your Extension of Stay.
You can directly apply for a new Extension of Stay, if you can not meet any of the requirements you will get Not approved and 7 days to leave the country.
Waiting for a visa for another country is no legit reason to apply for an Extension of Stay.
You have to cancel your work permit and take the documents to the Immigration Office to cancel your Extension of Stay based on being employed.
You can try to apply for a new Extension of Stay based on being unable to travel, if not approved you wil get a new stamp: application not approved and 7 days to leave the country. Land borders are open, I guess it is possible to leave within 7 days.