games: the buy-in and the rake each player sees are their own, not the table's

The two-browser pass found it: at a table two humans share, the felt quoted
each of them the pair's total. "Bought in for 200" to a player who put in 100,
and a session-rake line that climbed on a pot the other one won.

Both were table totals the view read straight off the engine — correct while a
table had one human, wrong the moment it had two. Fixed along the border it
already draws: bought_in is border accounting, so it comes from the viewer's own
game_seats.staked; session rake is a within-table event, so it rides a new
per-seat Seat.Paid beside the audit's table-total s.Paid.

And top-up never grew game_seats.staked, so the storage invariant drifted by
every top-up and the felt under-reported the buy-in — it does now.

Claude-Session: https://claude.ai/code/session_013M5nD7PgUboJXoDcYHzpuJ

internal/games/holdem/holdem.go

@@ -101,6 +101,7 @@ type Seat struct {
 	Bet   int64         `json:"bet"`   // put in on this street
 	Total int64         `json:"total"` // put in across this hand
 	Won   int64         `json:"won"`   // taken out of the pot this hand
+	Paid  int64         `json:"paid"`  // rake lifted from pots this seat has won, all session
 	State SeatState     `json:"state"`
 	Acted bool          `json:"acted"` // has chosen to do something this street
 }