Can I change from a Non Immigrant B visa to a tourist or long stay visa without leaving Thailand?

There is no grace period. The moment the reason for your extension ends, your extension is void. So even if your extension is good until February of next year, if your employments ends today, you must leave Thailand by today or make other arrangements. You are overstay as of the next day.

To apply for the Covid extension as Bobby mentioned, you will need to bring your cancelled work permit to immigration to cancel your extension based on the non-B, and then immediately apply for a Covid extension. If you can get paperwork from your company ahead of time saying you will stop working on xxx date, you can get your work permit cancelled about a week ahead of time and bring all the paperwork to immigration and also get that cancelled ahead of time, and then they will stamp you in until the date on the cancellation. You can then either immediately apply for the Covid extension or use the extra ~week of time to figure something else out.

You cannot get a tourist visa inside Thailand. Up to January 25 you can apply for the 60-day covid extension which will give you breathing space whilst you plan. What exactly do you want to do in Thailand?