We can use JSOM to achieve it. The following code for your reference.
<script type="text/javascript">
ExecuteOrDelayUntilScriptLoaded(retrieveWPProperties, "sp.js");
function retrieveWPProperties(){
var pageurl=_spPageContextInfo.serverRequestPath; //current page
var currentCtx = new SP.ClientContext.get_current();
var pageFile = currentCtx.get_web().getFileByServerRelativeUrl(pageurl);
var webPartManager = pageFile.getLimitedWebPartManager(SP.WebParts.PersonalizationScope.shared);
var webPartDefs = webPartManager.get_webParts();
currentCtx.load(webPartDefs, 'Include(WebPart.Properties)');
currentCtx.executeQueryAsync(
function () {
if (webPartDefs.get_count()) {
for (var i = 0; i < webPartDefs.get_count() ; i++) {
var webPartDef = webPartDefs.getItemAtIndex(i);
var webPart = webPartDef.get_webPart();
var properties = webPart.get_properties();
//console.log(JSON.stringify(properties.get_fieldValues())); //print all properties
if(properties.get_fieldValues().Title=="Content Search"){
var resultsPerPage=properties.get_fieldValues().ResultsPerPage;
alert(resultsPerPage);
}
}
}
else {
console.log("No web parts found.");
}
},
function (sender, args) {
console.log(args.get_message());
});
}
</script>
