I want to upload pictures to Photos for storage but not have them auto-add to my iPhone

Congratulations on your new MacBook Air! As muguy suggests, you can have multiple libraries on your Mac, even though a phone or iPad can have only one. Many of us have several Libraries-- I have a Library of my Wife's old family pictures, and I have another of my own family's old pictures, and also I have a Library of vacation and current family pictures. That's too many (sometimes not so interesting) pictures to sync with my phone and iPad, so I have a Favorites Library, and that's the one that shows on all my devices. I copy to it my favorite pictures from the other Libraries.

My Favorites Library is designated as my System Library-- it's the System Library that is synchronized with iCloud. You identify your System Library in Mac Photos>Settings>General. Note here that "Make a System Photo Library" is grayed out below, because it already is the System Library.

You can make a new Library by closing Photos and then option-clicking on the Photos app. You can name it something descriptive. Many of us use the trusted 3rd Party app PowerPhotos ($30) to make copying pictures between Libraries super simple, but you can also use Photos itself to Import pictures from other Libraries.

You are thinking of your Library on your Mac as a backup but, if that's what you want, you need to be sure that in Mac Photos>Settings>iCloud you hove "Download Originals" checked.

If you instead have "Optimize Storage" checked, then you will only be "backing up" smaller sized copies of your original pictures. Also, you should keep in mind that if you delete a picture from your Library on your iPhone, then it will be deleted on you Mac-- the Mac is a backup against a car running over your phone (you'll still have the pictures), but it isn't a backup against mistakes. For that you need an external drive and periodic copies of the Library. "Time Machine" is the Mac system that does that.

If you enable cloud photos, anything in your system library is synced across devices automatically. If you wish you can create a second (or third, fourth etc.) library that does not sync to iCloud and keep photos there.

I swear, this extra post is not my fault.