Can I Change Schools While on a Non-B Visa in Thailand Without Leaving the Country?

If you have the actual 90-day non-B visa, then there's nothing you can do but leave Thailand.

If you are on a work extension, then it's possible for your to cancel your extension, and then apply for a new extension based on work. But that is only possible if both schools and potentially both immigration offices are willing to help and coordinate to make it happen. You would need to get documents from your current school stating your last day of work, and then use that documentation to cancel your existing work permit and work extension at the immigration office that issued them. You can sometimes do this a week ahead of time. Then you would need to take the documents from your new school to their immigration office and apply for a new extension based on working for your new job. As I said, the immigration offices and the schools would all need to cooperate to get this done.

The other options is going to get a new non-B outside of Thailand. If you're currently on the 90-day non-B visa then you just leave Thailand and it's fine. If you're on an extension then you MUST cancel that extension before you leave. Then you get the documents from your new job and travel to whichever country you will be using to apply for the non-B visa. Submit the request through the e-visa system. If you go to Laos, it's normally 3-5 working days for a non-immigration visa.

In theory you can return as a tourist and apply to convert to non-B visa inside of Thailand, but most employers cannot or will not support this, because it requires a LOT more paperwork than applying at the embassy. Many companies cannot supply the correct paperwork because of how much it takes, and for those that can, they don't want to do it because it requires a lot of work. Easier to just send you outside of Thailand to get a new visa.

Isn’t the land border already closed?

like the policy has changed recently to denied visa run at the land border.