What type of visa am I currently on and do I need to leave Thailand to obtain a work permit?

>but I am wondering what visa am I classed as being on now

You do not have a visa right now, you have a 60 day extension of stay based on COVID-19. This extension of stay does not allow you to work.

>But I have been told that I have to leave the country because I need to be in Thailand on a Non Immigration visa first to get a work permit

That would be between you, your employer, and your immigration office. Some can get the visa or extension of stay, and some can't.

The criteria to get a Non-B visa inside Thailand is much higher then getting it outside of Thailand, which is why most businesses send their employees out of Thailand (generally to Laos) to get the visa. However, the borders to Thailand are now closed, and that's no longer an option.