csis: Start set member search when first device is connected

With this patch we start active search when first set member is fully
connected and all the characteristic are read.

Bug: 281119807
Test: atest bluetooth_csis_test
Test: atest BluetoothInstrumentationTests
Tag: #feature
Change-Id: I419714d51e844f78e2bbd401bd7b2cdc4f1934f8