Try this URL hash with URL query. Put it manually at the end of the URL. Save the URL, maybe as a bookmark.
#?period=week
#?period=month
examples:
current week: https://demo.matomo.cloud/index.php?module=MultiSites&action=index&idSite=1&period=day&date=today#?period=week
current month: https://demo.matomo.cloud/index.php?module=MultiSites&action=index&idSite=1&period=day&date=today#?period=month
or change the URL query value:
current week: https://demo.matomo.cloud/index.php?module=MultiSites&action=index&idSite=1&period=week&date=today
current month: https://demo.matomo.cloud/index.php?module=MultiSites&action=index&idSite=1&period=month&date=today