What do I need to prepare before entering Thailand for a Visa on Arrival and applying for an Ed Visa?

Correct, country is fully open nothing needed except passport, visa (if required) and an onward plane ticket if arriving by air and without a visa. Even a mask isn't required unless your airline requires it.

Question.... Some 7 years ago, I registered with my local immigration office my new address... with the homeowner. That address has not changed. I received a stamped slip (like the bottom of a 90-Day report) with said notification from them. Someone told me that there is a new one (a full-sized form) and that the older one is not always being accepted. Is this true? For I have never seen one in the 12 years I have been here. However, it would not surprise me as this is Thailand and things change from one minute to the next. I have to renew my licenses and do not want to go in empty handed... so to speak.

It sounds like you're arriving visa exempt and not visa on arrival.

With even 1 covid stamp in your passport you have a high chance of getting pulled out of line and questioned about why you're in Thailand again.

You might want to make sure you have the 3 proofs that immigration can ask for if they're looking for a reason to deny entry.

1) proof of funds (20,000 baht or equivalent in another major currency in CASH only)

2) Proof of leaving Thailand within 45 days

3) Proof of lodging (hotel reservation for at least the first few days)