Development of a personalized scheduler UI within Power BI to grant users stipulated time intervals for data updates or report refreshing can only be done indirectly through Power BI. However, using third-party tools with integration with Power Automate or other scheduling platforms could be a way. Here's how you could carry it out:
Applying Power Automate for scheduling: Power Automate can be used as an integrative technique for building automated workflows for data refresh and/or report updates according to the user. A user could, for example, view that there is now a Power Automate flow based on a time of day (like daily or weekly) or in response to a particular trigger (for instance, a button click on a Power BI report).
Custom UI by Power Apps: By offering an interactive interface to the users, Power Apps can help develop a custom UI in which users can have an option or choose when the refresh of data is to occur and then add the Power Automate actions that would trigger the activity. One could have a form designed in Power Apps that collects scheduling preferences and then schedules those in Power Automate for a data refresh.
Consumption of APIs and External Systems—If the user requires complete flexibility, he can also use Power BI REST APIs or Azure Logic Apps to schedule report refreshes. These can then be tied into a web-based UI (outside of Power BI) that enables users to configure refresh schedules.
Power BI Service Refresh Schedules: Power BI presents an option to schedule dataset refresh directly within the Power BI Service. He can configure refresh frequency (daily, weekly) and time windows, but this will not provide a personalized interface for end users to select schedules dynamically within a report. Instead, he has to use the standard scheduling interface within the service.
In summary, while there is no custom-built-scheduler UI within the report with Power BI, linking it with Power Automate and Power Apps to have user interaction and scheduling capability is one viable option. You will need Power Automate, Power Apps, and probably some external tools or APIs to build the functionality.
