Without a picture of the tree, and closeups of leaves and fruit, it is not possible to assess the problem.  The quick change suggests that there is an underlying problem that is killing the tree.  The following website has drop-down menus that will help you gather more information.  Look especially at the “branch dieback”  area.

https://apps.extension.umn.edu/garden/diagnose/plant/fruit/apple/index.html

Thanks for your response. I was not able to upload photos to the form but have attached them here. As you can see, there are only a few shriveled leaves at the end of each branch. The trunk and bark elsewhere on the tree look fine

It could be winter injury.  I would give it a chance to leaf out again but I am not optimistic that it will survive.  Can you send a picture of the base of the tree?  Another possibility is that it has developed circling roots that are strangling the tree but this doesn’t usually happen that suddenly. It is also common that dying trees may push out an initial leaf display by using all the stored nutritients and then die.  There may be another root issue as well. 

I can't take a picture of the base of the tree because we have one of those plastic wraps around it for rabbit protection and I can't move it. I'll take your advice to wait and see what happens through the rest of the summer but, like you, I'm not optimistic. Someone else asked me if I have jumping worms in our soil. I don't know whether we do or not, but could that cause tree death?

Jumping worms don’t harm trees directly like Emerald ash borer.  They degrade the soil and remove nutrients.  The following worm site shows you what to look for.  If you see soil that looks like coffee grounds they are likely present. Dig up some soil away from the tree so as not to disturb the roots and check it out.
While jumping worms could be indirectly involved it is unlikely that they caused rapid change like you are observing.  I would be very curious is there is bark damage under your plastic wrap.
https://extension.umn.edu/identify-invasive-species/jumping-worms

No, no damage to bark under the plastic wrap. My husband took it off after winter but we put it back on because the rabbits have been devouring everything. I peek under it and bark is okay

Aaaagh, I was wrong. I took the wrap off and found this destruction. I think it's actually old rabbit chewing from before we bought the wrap. It looks like it's gotten worse though--maybe bugs got in?

Yes, this is the cause of the tree dying.  It will not survive because the injury disrupted the flow of nutrients from the roots to the branches and the ability of the tree leaves to make sugars and send them back to the roots-technically the cambium layer of the tree.  

Back to your original question. Is this likely to affect anything else you grow there?  No it will not.  Just an observation-you will have a better root system if you move the tree farther from the fence. And rather than tree wrap use a fence to prevent this on future trees. See website below. Darn those rabbits!

https://extension.umn.edu/yard-and-garden-news/winter-protection-plants

Thanks for all your help. I planted the tree that close to the fence because originally I tried to espalier it, but gave that up when the tree got too tall. The rabbits have been extremely destructive in our yard, and I've tried everything to deter them. Previously they tunneled under and actually ate holes in a fence. I have tried live traps (not large enough for adult rabbits and babies are not heavy enough to trip the trap), various strong smelling herbs and spices, coyote urine. Rabbits--73, Me--0.

How frustrating!   I too have had damage even with my best efforts to use the same strategies you used.  My current strategy is to use repellents.  The following websites may be of interest.
1. https://www.dnr.state.mn.us/livingwith_wildlife/rabbits/index.html
2. https://extension.umn.edu/yard-and-garden-news/winterizing-plants-animal-damage