Apple's family sharing is complex and problematic. Family member charges are paid first from the Apple Account balance then secondarily to the Family Organizer account. Charges for members under 18 can require pre-authorization, but this cannot be done for over 18. The user interface for viewing Apple Account balances is obviously an old hack that would never pass any true review.
The Family Organizer receives emails with family member transactions on them. There's no comprehensive historic view of all family transactions however. A support article recommends using https://reportaproblem.apple.com, but that has only a 90 day history. Each family member can see their own transaction history on their Apple device, there is no web interface I know of for this comprehensive history. Recurring subscriptions are billed to the organizer but may be viewable only from the member account.
Essentially if a Family Organizer wishes to review family charges they need to do so within 90 days and they need to use reportaproblem.apple.com. Tracking emails is a less effective approach. To review older purchases the Organizer will need to use a family member's device or macOS account.
PS. Apple managed Subscriptions appear in the iOS/macOS subscription list, but 3rd party (ex. YouTube channel) subscriptions only. show up in the User's account view. You will see the recurring charge (monthly, etc) in reportaproblem.apple.com. Subscriptions must be managed in the host app, Apple only handles the billing.