We now have a parameter that will be used in a control you can use to change the date format. We've set the "backend" to change the date format, now we need to take care of the "frontend" if you will.
2. Build a calculated field as a dimension
So now, back to your data source. Please Add a formula and use the following formula (please refer to Google Looker Studio documentation to find the right formats that serve your needs), so your dimension is linked to your newly created parameter. When you'll change your parameter, the truncated date used will change. Again, to make it work across data sources, please create a new field in each data source with the same ID. Very important, SAME ID:
WHEN date_toggle="Year View" THEN DATETIME_TRUNC( Date,YEAR)
WHEN date_toggle="Month View" THEN DATETIME_TRUNC(Date,MONTH)
WHEN date_toggle="Week View" THEN DATETIME_TRUNC(Date,WEEK)