Do I need to transfer my visa extension to a new passport before traveling to Malaysia for a visa exempt entry to Thailand?

Go to Immigration to transfer your current stamp to the new passport, as in the moment you get the new one the old one is voided. In addition, new passport implies a new number, usually you can change passports in airports (leave with one, enter with another) but better to play in the safe side for this matter. And, it's possible that you have some issues on leaving on a voided passport because where will the exit stamp go?

To transfer the stamp is a fast task. It took me like 25 minutes in Chiang Mai a couple of months ago, not sure about the queues in BKK but usually there are at least one desk specifically for this task.

By the way, it doesn't matter if your extension is near to finish or still have 11 months on it: this is a kind of a binary thing, it is over or it is not over. "Almost over" is not a state for this matter.

Regarding that bounce... on theory it's possible, but again you would play it safer if you stay overnight in Malaysia. Just leave the airport, go for some shopping in KL or some food in Penang depending or your flight, and come back the next day, not need to hurry up and make immigration officers to wonder (I'd spend at least one week, both KL and Penang are worth that time, but I don't know your circunstances)

If you're going to have a new contract on March maybe your company can write a letter/pre-contract for you just in case the immigration officer queries you about why you were working and now come back as a tourist - but don't show it unless required.

My advice is get the stamps transferred to the new passport and cancel the extension.

remember stamping out on an extension does NOT officially cancel it, it just stamps you out 😕

so take documentation from your employer stating you stop work on xx date, go to the immigration office and cancel the current extension, and then leave.