What KPIs do you use that directly tie to adoption vs. correlate to adoption (e.g. we send an email campaign and in the same month adoption increases 5% - there is no way to prove the email conclusively led to 5% adoption)

I love this question, but also don't love an environment that needs to conclusively prove one team is responsible for adoption! Ideally you're just using metrics to guide whether you should do more or less of a thing, rather than as an award system

But even so, the best way to figure out whether you should send more launch emails in future, is just use a control. Start with a pre-launch pool of say 50 users that you think having the highest likely of adoption. Send the email on Day 1 to the first 25 and on Day ~8 to the remaining 25. Track when adoption happened for each group—was it just after the email? Or did they organically find the new solution in product and purchase/begin using anyways?

But if it were me I might just do the email as a formality tbh, and err on the side of in-product messaging. If you have the right tech, you'll be able to see who was served the notification, whether they clicked it, and exactly what they did after.