Will the TMC2226 enter Test Mode under normal operation? Under what conditions will it enter this mode?

It is very unlikely the TMC2226 will enter in test mode it will only activate when the voltage on both 5VOUT and VCC_IO are exceeded at the same time. Under normal conditions it is not possible. It is only mentioned for troubleshooting intentions.
Please find absolute maximum ratings below and TMC2226 datasheet TMC2226 Datasheet (analog.com).