This evidence can only come from financial accounting. Amazon does not report OpenSearch results separately so you’re looking for data that does not exist in a public form. It’s a waste of time.
> This evidence can only come from financial accounting.
That's not true—we're talking about brand value, not financial value of the product. If AWS switched over to offering ElasticSearch again (not that they will) and ditched OpenSearch, I have no reason to believe that their financial numbers would go down a bit.
Brand value is nearly impossible to measure, but to the extent that you can it'd be by measuring perception among those outside the company, not through an accounting of the company's actual revenue.
Think of it this way: the brand LENRUE [0] is worth approximately zero. The company that makes these products could rebrand tomorrow and their revenue stream wouldn't take a hit in the slightest. But the company presumably actually makes some amount of money.
For Elastic vs OpenSearch, the brand value of the two products should be loosely comparable by looking at some measures of public perceptions, and I can't find any measurement that would suggest OpenSearch is in the lead.