feat: Add request start time context key and update middleware

- Introduced a new constant `ContextKeyRequestStartTime` to store the request start time in the context, enhancing request tracking.
- Updated the `Distribute` middleware to set the request start time in the context using the new constant.
- Modified the `GenRelayInfo` function to retrieve the request start time from the context, ensuring accurate timing information is used in relay operations.

middleware/distributor.go

@@ -12,6 +12,7 @@ import (
 	"one-api/service"
 	"strconv"
 	"strings"
+	"time"
 
 	"github.com/gin-gonic/gin"
 )
@@ -112,6 +113,7 @@ func Distribute() func(c *gin.Context) {
 				}
 			}
 		}
+		c.Set(constant.ContextKeyRequestStartTime, time.Now())
 		SetupContextForSelectedChannel(c, channel, modelRequest.Model)
 		c.Next()
 	}