You may want to reach out to your client and ask them to close the contract if they no longer have any work for you, or if they do, they can temporarily pause the contract and resume it once they are ready to give you new tasks to do.
Although I don't believe you'll be able to get a straight answer from upwork on this (they are fairly adamant about keeping their jss computation method under wraps) in my experience, I can say yes - that does affect your jss score - though I couldn't tell you how badly.
My only advice to you is this - be very careful on terminating the job yourself, should that become your only option. I did this for a few longstanding paused contracts with no activity - all at once - and found out the hard way that an excess of 'no feedback' hurts you far more than a few open contracts gathering dust.
So unless you're very confidant that you have a high percentage of good feedback already - i.e. at least 80% - or 4 out of 5 (and it looks like you have been a member starting in May, so I'm guessing you can't have more than 2 or 3 individual feedback pieces on jobs?) don't close that contract.
I stand corrected - Valeria's answer was actualy fairly straightforward.
However - keep in mind I got the same answer when I originally asked - and cancelling the contracts got me into a world of hurt.
I conscientiously try to avoid paused contracts.
Contracts are paused after one month of activity.
If I am done with work for a client for what seems to be the foreseeable future, I ask them straight out to close the contract. Even if they are certain they'll need me later (but they're not sure when). I point out that they can easily set up a new contract when they need me.