I would try with the SETV as much as possible. If it doesn't work out, you can come in on visa exemption.
The problem with switching to an ED or B visa with a visa exemption is that you have maximum 60 days. Which is not a lot of time for many schools/companies, since it can take a number of weeks to prepare the documentation—plus the 15 days left of your visa needed to apply. It's doable, but not a lot of time. (There is always the COVID extensions, but might not be available in Feb/March when you'll need it. If that's the case, you will need to leave Thailand.)
SETV is 60 days, and can extend another 30 days for 1,900฿ at an immigration office. Visa exemption is 30 days, and can extend another 30 days for 1,900฿. 90 days instead of 60 total.
If you are 100% sure you only need to stay 45 days, then VE should be fine. If you are here and plan to stay a few weeks more, and you chose the VE, then that's that.
Tourist visa to Non-Immigrant B visa is possible. About tourist visa to ED visa, it was possible in the past. There were changes with the Ministry of Education in 2020 about not giving ED visas to private language schools. I have no idea what has changed since then. Contact other schools and see what they say.
Yes. COVID extensions would give you another 60 days. The last announcment they said they are going to be a bit more strict. You could be asked by an IO for a flight out of Thailand before giving you it.
You can change from a tourist visa to a Non-Immigrant B visa inside Thailand. However, it can take 2-7 weeks for a school to prepare the needed documentation to do so.
With 47 days, you don't have much time. However, you can take COVID extensions, which are available until Jan. 25.
The school/company that told you that probably doesn't have very good visa staff. Find one that does.
