That's great news overall!!!
A few comments...
Ph varies throughout the day from 8.15 to 8.3
Alk 9.65 trying to bring down to around 7.5
Nitrate 2
Cal 455
Temp 79
Phos 9 ppb or 0.028
Is there anything I can do about the cyano or just let it run its course? It's clearly not due to high nutrients.
I'd probably stop watching pH.
Try your best to dose nutrients daily so they don't bottom out anymore....both test numbers are still pretty low, so would be in potential danger of doing so.
I also wouldn't worry too much about alk. With nutrient no longer out of whack (in particular, phosphates) is shouldn't be an issue.
Focus on keeping nutrients stable and staying on top of new algae growth. Keep all algae under control/keep them from dominating by manual methods...plucking, scrubbing and siphoning...as well a CUC upgrades as needed.
(Some, maybe all, algae blooms resolve totally without intervention as long as the environmental conditions are corrected, but usually we can help progress along. In some cases help is a requirement.)
And yes, cyano should just be a phase. Not unlike what a new tank goes through, but probably more pronounced since the tank isn't new/empty.
So don't be surprised if you see the "classic" transition from cyano to green algae to coraline. Don't try to stop it, just help it keep progressing with the methods listed above. Methods here
Algae Cure!! Spot Treating Algae With Peroxide can be used as well if it seems necessary.