Perhaps you can make use of the subfilter as documented here? Keep the limit high and use the days filter in the sub filter to limit it to the last seven days days[-7]
See $:/core/ui/SideBar/Recent it contains;
<$macrocall $name="timeline" format={{$:/language/RecentChanges/DateFormat}}/>
Perhaps clone this, change the caption to week and edit as follows
<$macrocall $name="timeline" limit=200 format={{$:/language/RecentChanges/DateFormat}} subfilter="days[-7]"/>
An additional tab means the default remains as is.
This seems to be doing the job.
However perhaps if one could change the number of days, eg edit or buttons for day/7days/14days/31days/62days/
Of course other subfilters could be used to filter on current month, current week number etc…