What is the platform made of ?
SUPERGLUE IS VERY HIGH IN TOXIC VOLATILES .
So not a suitable adhesive IMO to use in any enclosed space where ventilation will be poor.
Also , it's a space filler type adhesive , relies on filling the gap at a break very closely and it relies more on air pressure to hold the parts together , and is not all that strong under torque or tension.
I think a better adhesive will be 5min 2 part araldite , but be careful of using this in a confined space or exposing a reptile to it long term ( toxic ingredients and it also outgases over a period of time while and after setting ).
I'd suggest replacing the broken platform entirely to be safe.