The surge protector supplied with your TT will only protect against surges, it will not protect against high/low voltage, reverse polarity, open neutral, open ground, etc.
The upgraded surge protector you mention will only protect against surges but no other electrical problems. The LEDs will tell you if there is a problem but the device will not protect your TT from the problem.
I'd recommend you get an EMS such as this one
https://www.progressiveindustries.net/ems-pt30x
There is a hardwired version also.
It is more expensive but the EMS will disconnect or prevent power from reaching the TT if there is an electrical problem with the supply and will better protect your electronics and electrical equipment such as the AC.
Have fun camping with your new setup.