Requirement
We need to change the standard status field, which is not displayed on the task form based on the custom status field.
Solution
We can create a user event script to update the standard field for this purpose.
/**
 * @NApiVersion 2.1
 * @NScriptType UserEventScript
 */
define(['N/currentRecord', 'N/record'],
    /**
 * @param{currentRecord} currentRecord
 * @param{record} record
 */
    (currentRecord, record) => {
        /**
         * Defines the function definition that is executed after record is submitted.
         * @param {Object} scriptContext
         * @param {Record} scriptContext.newRecord - New record
         * @param {Record} scriptContext.oldRecord - Old record
         * @param {string} scriptContext.type - Trigger type; use values from the context.UserEventType enum
         * @since 2015.2
         */
        const afterSubmit = (scriptContext) => {
            try {
                if (scriptContext.type === 'create' || scriptContext.type === 'edit' || scriptContext.type === 'xedit' || scriptContext.type === 'copy') {
                    var taskRecord = scriptContext.newRecord
                    var taskId = taskRecord.id
                    var custStatus = taskRecord.getValue({
                        fieldId: 'custevent_jj_status'
                    })
                    log.debug('custStatus', custStatus)
                    var stdStatus=taskRecord.getValue({
                        fieldId: 'status'
                    })
                    log.debug('stdStatus', stdStatus)
                    if (custStatus == '1') {
                      record.submitFields({
                            type: record.Type.TASK,
                            id: taskId,
                            values: {
                                status: 'NOTSTART'
                            },
                            options: {
                                enableSourcing: false,
                                ignoreMandatoryFields : true
                            }
                        });
                    } else if ((custStatus == '2') || (custStatus == '3')) {
                        log.debug('In 2')
                        record.submitFields({
                            type: record.Type.TASK,
                            id: taskId,
                            values: {
                                status: 'PROGRESS'
                            },
                            options: {
                                enableSourcing: false,
                                ignoreMandatoryFields : true
                            }
                        });
                    } else if ((custStatus == '4') || (custStatus == '5')) {
                        log.debug('In 3')
                        record.submitFields({
                            type: record.Type.TASK,
                            id: taskId,
                            values: {
                                status: 'COMPLETE'
                            },
                            options: {
                                enableSourcing: false,
                                ignoreMandatoryFields : true
                            }
                        });
                    }
                }
            }
            catch (e) {
                log.debug('Error@Aftersubmit',e)
            }
        }
        return {afterSubmit}
    });