fix(co-sign): fix session start logic to check all registered participants

- CanStart(): Check if all registered participants have joined, not based on T/N
- AddParticipant(): Keep N as max limit (API handles T vs T+1 validation)
- AllPartiesReady(): Check all registered participants, not based on T/N
- This approach works for both co-managed (T parties) and persistent (T+1 parties) signing

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/mpc-system/services/session-coordinator/domain/entities/mpc_session.go

@@ -98,6 +98,9 @@ func NewMPCSession(
 
 // AddParticipant adds a participant to the session
 func (s *MPCSession) AddParticipant(p *Participant) error {
+	// For sign sessions, the max participant check is handled at the API level
+	// (co-managed uses T, persistent uses T+1)
+	// Here we just prevent exceeding N which is the absolute maximum
 	if len(s.Participants) >= s.Threshold.N() {
 		return ErrSessionFull
 	}
@@ -140,26 +143,22 @@ func (s *MPCSession) UpdateParticipantStatus(partyID value_objects.PartyID, stat
 
 // CanStart checks if all participants have joined and the session can start
 func (s *MPCSession) CanStart() bool {
-	// Determine required participant count based on session type
-	// For keygen: all N parties must participate
-	// For sign: only T parties participate
-	requiredCount := s.Threshold.N()
-	if s.SessionType == SessionTypeSign {
-		requiredCount = s.Threshold.T()
-	}
-
-	if len(s.Participants) != requiredCount {
+	// Session can start when all registered participants have joined
+	// The number of participants was determined at session creation time:
+	// - For keygen: N parties are registered
+	// - For sign: T or T+1 parties are registered (depending on the signing flow)
+	// We don't need to check against T or N here - just verify all registered parties have joined
+	if len(s.Participants) == 0 {
 		return false
 	}
 
-	readyCount := 0
 	for _, p := range s.Participants {
-		// Accept participants in either joined or ready status
-		if p.IsJoined() || p.IsReady() {
-			readyCount++
+		// All participants must be in joined or ready status
+		if !p.IsJoined() && !p.IsReady() {
+			return false
 		}
 	}
-	return readyCount == requiredCount
+	return true
 }
 
 // Start transitions the session to in_progress
@@ -265,7 +264,9 @@ func (s *MPCSession) MarkPartyReady(partyID string) error {
 
 // AllPartiesReady checks if all participants are ready
 func (s *MPCSession) AllPartiesReady() bool {
-	if len(s.Participants) != s.Threshold.N() {
+	// Check that all registered participants are ready or completed
+	// The participant count was determined at session creation time
+	if len(s.Participants) == 0 {
 		return false
 	}
 	for _, p := range s.Participants {