refactor: improve cycle generation code quality and documentation

- Remove Process.sleep calls from integration tests (tests run synchronously in SQL sandbox)
- Improve error handling: membership_fee_type_not_found now returns changeset error instead of just logging
- Clarify partial_failure documentation: successful_cycles are not persisted on rollback
- Update documentation: joined_at → join_date, left_at → exit_date
- Document PostgreSQL advisory locks per member (not whole table lock)
- Document gap handling: explicitly deleted cycles are not recreated

docs/membership-fee-overview.md

@@ -120,7 +120,7 @@ This document provides a comprehensive overview of the Membership Fees system. I
 ```
 - membership_fee_type_id (FK → membership_fee_types.id, NOT NULL, default from settings)
 - membership_fee_start_date (Date, nullable) - When to start generating membership fees
-- left_at (Date, nullable) - Exit date (existing)
+- exit_date (Date, nullable) - Exit date (existing)
 ```
 
 **Logic for membership_fee_start_date:**
@@ -167,16 +167,17 @@ value: UUID (Required) - Default membership fee type for new members
 
 **Algorithm:**
 
-Lock the whole cycle table for the duration of the algorithm
+Use PostgreSQL advisory locks per member to prevent race conditions
 
 1. Get `member.membership_fee_start_date` and member's membership fee type
-2. Generate cycles until today (or `left_at` if present):
-    - If no cycle exists:
-      - Generate all cycles from `membership_fee_start_date`
-    - else:
-      - Generate all cycles from last existing cycle
-    - use the interval to generate the cycles
-3. Set `amount` to current membership fee type's amount
+2. Determine generation start point:
+   - If NO cycles exist: Start from `membership_fee_start_date`
+   - If cycles exist: Start from the cycle AFTER the last existing one
+3. Generate cycles until today (or `exit_date` if present):
+   - Use the interval to generate the cycles
+   - **Note:** If cycles were explicitly deleted (gaps exist), they are NOT recreated.
+     The generator always continues from the cycle AFTER the last existing cycle.
+4. Set `amount` to current membership fee type's amount
 
 **Example (Yearly):**
 
@@ -246,7 +247,7 @@ suspended → unpaid
 
 **Logic:**
 
-- Cycles only generated until `member.left_at`
+- Cycles only generated until `member.exit_date`
 - Existing cycles remain visible
 - Unpaid exit cycle can be marked as "suspended"