Hi!

Would anyone happen to know of some website or program where you can log flights and batteries in order to maintain them properly?
Basically something that will help remind me to cycle a battery after three months of storage for example.

I don't know of any, but if you want more response you might be better off posting your question in the 'products' section of this forum.
That is way more active.
Just create a new thread here : https://forum.dji.com/forum-129-1.html and select the right category / subcategory.

I use airdata.com for that,   the free account keeps the last 100 flights of data.

Mark each battery 1, 2, 3 etc with a cd marker so you know which is which.
Note using pencil & notebook the battery number (1, 2, 3...) date, flight length or % charge left when you landed. This is all in the app, before you shut down the drone.
It isn't rocket science.
It is so easy and quick to keep check on usage. Even if you lose the notebook, the number of charges is still available in the app when you power on the drone.