Can't create a RTC_DATA_ATTR var inside a class
You can't put an RTC_DATA_ATTR qualified variable inside a class because the class is stored in normal RAM. The RTC_DATA_ATTR qualified variable is, by definition, stored in RTC RAM.

The definition of RTC_DATA_ATTR includes a section attribute (__attribute__((section(".rtc.data")))) that tells the compiler where abouts in memory the variable should be stored (in this case the 8kiB of "slow" RTC memory). That is mutually exclusive with where the compiler decides to store the class.

It's like you have a diamond necklace which the has to be kept in a safe at all times, but you want to wear it around your neck whilst at the same time storing it in the safe. You can't do it.