Docs, gettext, and remaining test updates

- groups-architecture and membership-fee-architecture docs
- Gettext: add/correct German for authorization and membership fee type
- membership_fee_helpers_test and membership_fee_status_test adjustments

docs/membership-fee-architecture.md

@@ -334,20 +334,18 @@ lib/
 
 ### Permission System Integration
 
-**See:** [roles-and-permissions-architecture.md](./roles-and-permissions-architecture.md)
+**Status:** ✅ Implemented. See [roles-and-permissions-architecture.md](./roles-and-permissions-architecture.md) for the full permission matrix and policy patterns.
 
-**Required Permissions:**
+**PermissionSets (lib/mv/authorization/permission_sets.ex):**
 
-- `MembershipFeeType.create/update/destroy` - Admin only
-- `MembershipFeeType.read` - Admin, Treasurer, Board
-- `MembershipFeeCycle.update` (status changes) - Admin, Treasurer
-- `MembershipFeeCycle.read` - Admin, Treasurer, Board, Own member
+- **MembershipFeeType:** All permission sets can read (:all); only admin has create/update/destroy (:all).
+- **MembershipFeeCycle:** All can read (:all); read_only has read only; normal_user and admin have read + create + update + destroy (:all).
+- **Manual "Regenerate Cycles" (UI):** The "Regenerate Cycles" button in the member detail view is shown to users who have MembershipFeeCycle create permission (normal_user and admin). Regeneration runs with system actor; UI access is gated by `can_create_cycle`.
 
-**Policy Patterns:**
+**Resource Policies:**
 
-- Use existing HasPermission check
-- Leverage existing roles (Admin, Kassenwart)
-- Member can read own cycles (linked via member_id)
+- **MembershipFeeType** (`lib/membership_fees/membership_fee_type.ex`): `authorizers: [Ash.Policy.Authorizer]`, single policy with `HasPermission` for read/create/update/destroy.
+- **MembershipFeeCycle** (`lib/membership_fees/membership_fee_cycle.ex`): Same pattern; update includes mark_as_paid, mark_as_suspended, mark_as_unpaid.
 
 ### LiveView Integration
 
@@ -357,7 +355,7 @@ lib/
 2. MembershipFeeCycle table component (member detail view)
    - Implemented as `MvWeb.MemberLive.Show.MembershipFeesComponent`
    - Displays all cycles in a table with status management
-   - Allows changing cycle status, editing amounts, and regenerating cycles
+   - Allows changing cycle status, editing amounts, and manually regenerating cycles (normal_user and admin)
 3. Settings form section (admin)
 4. Member list column (membership fee status)