Unable to pass custom attribute "user role" as query parameter in Cognito Hosted Ui url

I am trying to pass the custom user attribute (custom:role) through Cognito hosted UI URL as a query param. Still, I cannot get the passed attribute in either lambda PreSign trigger or it is not being saved in user attributes.

I've added a custom user attribute as role and allowed to read and write permissions.

Here are some examples of cognito hosted UI and allowed callback URLs, I tried

1. https://${userPoolId}.auth.us-east-1.amazoncognito.com/signup?response_type=code&client_id=${clientId}&redirect_uri=${encodeURIComponent(redirectUri)}&state=${state}

Where const state = encodeURIComponent(JSON.stringify({ ["custom:role"]: "value" }))

ALLOWED URL: http://CALLBACK_URL/ROUTE&Istate%3D%257B%2522custom%253Arole%2522%253A%2522independent%2522%257D

2. https://${userPoolId}.auth.us-east-1.amazoncognito.com/signup?response_type=code&client_id=${clientId}&redirect_uri=${REDIRECT_URI}/ROUTE&role=value ALLOWED URL : ${REDIRECT_URI}/ROUTE&role=value

3. https://${userPoolId}.auth.us-east-1.amazoncognito.com/signup?response_type=code&client_id=${clientId}&redirect_uri=${REDIRECT_URI}/ROUTE&encodeURIComponent()user_attributes: { 'custom:role': 'value' })

ALLOWED URL : ${REDIRECT_URI}/ROUTE&encodeURIComponent()user_attributes: { 'custom:role': 'value' })

In the lambda function, I am just getting email attributes in user_attributes object from the request.

LAMBDA PRE SIGN TRIGGER Logs: 2023-03-31T07:04:57.154Z c74de25c-a20a-42d5-9af7-00ffc5dd062f INFO .....event.... { version: '1', region: 'us-east-1', userPoolId: 'us-east-1_iBb7CJZGw', userName: '86b6e63d-8309-42b4-8446-668b0c80b9e6', callerContext: { awsSdkVersion: 'aws-sdk-unknown-unknown', clientId: '6qciagr67e8kptsakeuk9h7mi7' }, triggerSource: 'PreSignUp_SignUp', request: { userAttributes: { email: 'voconefy@mailinator.com' }, validationData: null }, response: { autoConfirmUser: false, autoVerifyEmail: false, autoVerifyPhone: false } }