You can try to wrap the part containing special characters with double-quotes.
https://xxxx.sharepoint.com/sites/scr/_api/search/query?QueryText='scStatusOWSCHCS=Expired scContractRenewabilityOWSCHCS="Yes (Auto Renew)"'&selectproperties='Title,scContractRenewability,SPWebUrl,OriginalPath,ListItemID,ModifiedBy'&rowlimit=500
I create a Contract Renewability column in my list.
My test result:
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