JSON.deserialize() can be used in Salesforce Apex to parse Array payload in Apex REST API.

Please check the following Apex Class for reference.

Sample Apex Class:

@RestResource( urlMapping='/ApexRESTAPI/' )
global with sharing class RESTAPIController {
    
    @HttpPost
    global static void checkArrayInput() {
        
        String strResponse;
        Map < String, String > mapResponse = new Map < String, String >();
        RestRequest req = RestContext.request;
        String strReqBody = req.requestBody.toString();
        System.debug(
            JSON.deserialize( 
                strReqBody, 
                List < String >.class
            )
        );
        List < String > listInputs = ( List < String > ) JSON.deserialize( 
            strReqBody, 
            List < String >.class
        );
        
        if ( listInputs.size() > 0 ) {
            
            mapResponse.put(
                'message',
                'Received ' + listInputs.size() + ' items'
            );
            
        } else {
            
            mapResponse.put(
                'errorMessage',
                'Request Body is empty'
            );
            
        }
        
        strResponse = JSON.serialize(
            mapResponse
        );
        RestContext.response.addHeader(
            'Content-Type', 
            'application/json'
        );
        RestContext.response.responseBody = Blob.valueOf(
            strResponse
        ); 
        
    }
    
}

Output: