That’s such a rough way to start a vacation.
Even if the bag was scanned as arrived, it’s still technically missing from you. So it should be treated as delayed baggage at this point. The key thing is you already filed a report and have a claim number. That’s good.
For now, buy what you reasonably need. Clothes, toiletries, basics. Don’t go wild, but don’t suffer either. Keep every receipt. Delta usually reimburses reasonable interim expenses while the bag is delayed.
If the bag doesn’t turn up after a certain number of days, it moves from “delayed” to “lost,” and then compensation rules change. But most bags that are grabbed by mistake do come back once the other passenger realizes it.
I’d also:
Make sure your contact info is correct on the claim
Add a detailed description of the bag and contents in the app if possible
Check if you have credit card travel insurance as backup
It’s stressful, but odds are decent it shows up in a day or two once the mix-up gets sorted.