Section 38 ot the Immigration Law has not changed, as far as I know, but there have been changes in the procedures over the years. Currently, there is this on the website of the Immigation Bureau:
https://www.immigration.go.th/en?p=14721
Generally, the first application for a one-year extension of stay after entry with a non-O visa counts simultaneously as your notification of staying in Thailand longer than 90 days but there seems to be no written rule about this and some immigration offices may handle it differently.
Some immigration offices ask the applicant for a one-year extension of stay to come back 30 days after the application, others 30 days after the expiration of the current permission to stay.
You do not need an agent to apply for a non-O volunteer visa and therefore there is no agent to whom to pay a fee. Check with the Thai embassy or consulate where you plan apply what their requirements are and take it from there.
Is there perhaps some misunderstanding? Obviously, WU had to ask for your passport for identification, but did they in addition ask you to point to the page showing your current permission to stay?
With the link given in the OP, I get this error message:
Access denied
Error 14
tna.mcot.net
2022-12-08 12:44:51 UTC
Did that news article perhaps get censored?
Do I understand correctly that this is finally something where the requirements do not vary from one immigration office to the next? If this is the case, I say "well done"
Your daughter cannot travel "under" your Thai visa.
Depending on her intended length of stay in Thailand, she can travel without a visa, with a tourist visa, or with a non-O visa to visit family.