OK, what you have here is a Type BR panel with no main breaker. (You're backfeeding a branch circuit breaker, which is allowed as long as you make it so it can't be easily removed, hence that screw in the breaker).

I think this is the interlock you need:

https://www.homedepot.com/p/Eaton-Generator-Interlock-Kit-for-Back-Feed-BR-Load-Centers-BRMIKBR/205050848

Ok thanks for the helpful note. So how would that mount? It looks like I need to leave those 2 right slots empty so the switch can mount there, then move the range somewhere else. if this is the case then I cannot do that because the panel is full.

It goes where the main breaker is now, and the generator breaker needs to be in the slot immediately below that.

The hardest part is that it involves removing the main breaker. Unless you have an external disconnect (uncommon), you'll likely have to have the utility pull and reinstall the meter.

The instructions are here: https://www.eaton.com/ecm/idcplg?IdcService=GET_FILE&allowInterrupt=1&RevisionSelectionMethod=LatestReleased&noSaveAs=0&Rendition=Primary&dDocName=IL003003EN

Hi are you sure that I have to pull the main breaker? It looks like I just have to move the range and wire the generator where the range is. Therefore I slide the lock up once the main is off to be able to turn on the generator. The lock panel will mount right over the empty breakers. See below?

The picture looks right. I've never done one of these. All I was going on was the instruction that says you have to take out the backfed breaker to swap the hold down with the one that comes with the interlock. I guess if you're brave you can try doing that without cutting off the backfeed power, but I'm not (and the instructions say otherwise).

Ok I see it now. I wonder if that’s actually necessary, since there already is a retaining screw in the main breaker and I can add a separate retainer for the generator breaker?

Like I said, I've never done one of those, I'm just going by the instructions which you're pretty much obligated to follow. If it wasn't necessary, I don't have any idea why they would have provided a different hold-down and told you to replace it.