Is there a way to automate backups for my Jira Cloud site on a daily basis including pulling all the data and attachments?
Atlassian provides option to import-export xml however that cannot be automated as far as I know. Your next best bet to automate it by yourself would be Jira developer APIs (https://developer.atlassian.com/cloud/jira/platform/rest/v3/intro/).
Using APIs you can pull data to a greater extent. However it may not be as intuitive as you may want or how it used to be on the on-prem version of Jira server (DB backups). However you may want to plan the efforts & cost for the script maintenance, cataloging the downloaded data and maintaining the data for long term. You can find some details in this thread - JIRA with Python
Alternatively you may want to go for 3rd party apps in Atlassian marketplace which supports automatic/scheduled backups of Issues & Configuration, granular & full project restores, long term storage and secure offsite storage.
Disclaimer - I work at Revyz, we have developed a Jira app which solves this exact problem. We backup & restore Atlassian Jira along with other features as mentioned above. You may want to take a look at https://www.revyz.io/ & https://marketplace.atlassian.com/apps/1228694/revyz-backup-restore?hosting=cloud&tab=overview