"Ticket not issued"

I ran into this with tickets booked in advance by a tour company. You have a reservation, which you should be able to see with your confirmation #. You do NOT have a ticket, and probably won't have one issued until maybe 90 days before your travel date. At least, that was our experience.

Since you booked the entire trip through Delta. Since, Delta issued both a confirmation code and ticket number(s) for your trip the Delta app is what should use.

So I will get a boarding pass to scan on the Delta app for the KLM flights?

Maybe I’m misunderstanding this but if you booked your ticket thru Delta, Delta will issued you the boarding passes for all flights. Make sure you have the Delta App. From what we’ve experienced in the past, if you try to look up a flight on a partner airline with the booking number from the booking airline, the partner airline is not going to recognize it.

You should be able to check in the day before your flight and get boarding passes via Delta. I know for recent trip to Spain, we had some Delta flights operated by KLM, but they had Delta flight numbers and everything was in the app (I have the KLM app, just in case). And you can always check-in, then get printed passes at the airport kiosk if for some reason the KLM passes don't show up in your Delta app.

From what we’ve experienced in the past, if you try to look up a flight on a partner airline with the booking number from the booking airline, the partner airline is not going to recognize it.

I was able to do just that with Virgin Atlantic (booked all on Delta, used the Virgin app for the boarding passes for the Virgin portion). I think it's the highlighted "ticket not issued" on the KLM app that is throwing me. I don't recall that on the Virgin app.

And you can always check-in, then get printed passes at the airport kiosk if for some reason the KLM passes don't show up in your Delta app.

Thank you. Great point.

I did that same flight in September. ATL-AMS-BUD. My boarding passes were all in the Delta app.
I was also going to suggest getting printed boarding passes in ATL for all your flights, just for extra reassurance that you'll be able to board your flight to BUD. Though the gate for my BUD flight changed three times during my layover, so you'll have to keep an eye on the app and the overhead signs anyway.

And also
"so there’s literally no urgency today, but I somehow chose to fixate on it anyway." LOL. This is ME. 100%.

So I will get a boarding pass to scan on the Delta app for the KLM flights?

You should. But, as someone suggested pick up hard copies from a kiosk or check-in counter when you arrive at the airport. We do that a lot on international flights even if we have electronic boarding passes.

if you try to look up a flight on a partner airline with the booking number from the booking airline, the partner airline is not going to recognize it

Right, but if you enter the actual ticket number (not booking or confirmation number) on the partner airline website your reservation should pop up. You may also get a confirmation or booking number for the partner airline too.

We were flying home from Amsterdam in April on our multi trip ticket (LAX>Paris>AMS>LAX) booked through Delta. Airplanes were operated by Delta. The night before our flight I got this vague text saying that I should go to KLM at the AMS airport. I didn’t know what that meant. Did my Delta flight get cancelled, do I check in online through KLM? It was confusing. I reached out to this forum and was immediately put to ease when they said there are no Delta counters at Amsterdam; you just do everything in person at KLM. Checked in online on my Delta app. Scanned my tickets through the Delta app. The gate employees were KLM in KLM uniforms but in fact our plane was operated by Delta and our flight attendants had on Delta uniforms.
I don’t know if this helps ease your mind or confuses you, but thought I’d mention my experience. Since some of your flights are operated by KLM you can always print boarding passes at the airport if that helps alleviate worry. But I don’t think you have a thing to worry about. Your confirmation code is a Delta confirmation number so it won’t be a KLM confirmation code.

When you were talking to Delta and KLM, did they explain what "ticket not issued" means?

Digital tickets and Boarding Passes can’t always be accessed if your phone malfunctions, runs out of power or is damaged. Good ol’ paper copies of Boarding Passes are always a good idea as a backup.

Actually I found paper copies are more trouble than they’re worth. I haven’t printed a boarding pass in years and I’ve never had any problems. And if you do, there’s someplace at the airport to print it.

But if you're on RyanAir you will pay a pretty penny for issuance of a boarding pass at the airport, I believe--I think the fee is around $50 US.