I don’t understand what you don’t understand. The oura comparison is one they made and used “charging every day” as a reason to not use a rechargeable battery. If they took the oura hardware model and applied it to their voice recorder ring, you would be charging monthly if not longer.
TL;dr - There’s no reason to not have a rechargeable battery other than to create e-waste and “a revenue stream”.
That's total nonsense, you have to make it larger to include a charging mechanism (which would need to be proprietary to fit) and it's more difficult to manufacture in a water-tight way. They're spending significantly less on developing and building this than Oura has. Keep in mind Oura has raised over a billion dollars in funding.
The e-waste here is negligible. If you've ever tossed a laptop or phone you've effectively produced more e-waste than a lifetime of these little things. A single disposable AA battery is more waste by weight.