The MySafeTravel lists the policies for traveling from Singapore quite clearly:
https://mysafetravel.gov.my/travel-from-sg

No matter what, you will need MySejahtera and insurance (as stated on the link above).

What type of registration confirmation are you waiting for? You just install the app, create a profile, and fill out the travellers card. I don't think you need to wait for anything for that. (verifying vaccine might take some time, but there are plenty of posts in this thread discussing that already).

I looked into visiting East Malaysia (Sarawak and Sabah). As far as I can tell, if you travel domestically from, for example, Kuala Lumpur to Kita Kinabalu, then there are no restrictions or test requirements. But I'm not 100% sure... I also looked into Langkawi, but I couldn't find any information regarding domestic travel to Langkawi. It's all quite unclear.