It’s easy since I spent only 30+ minutes. So try it before read my thought and you’ll have some fun.
I ‘guess’ it would be very slow to check all primes one by one.
[1..9] are all Harshad numbers (seeds).
Take one seed, add one digit to it and check if it’s valid. For example, take 2, check [20..29]. All valid numbers are new seeds.
Check if a new seed is also a strong Harshad number.
If a seed is a strong Harshad number, append one digit to it and check if it’s a ‘strong, right truncatable Harshad primes’. For example, 201 is a strong Harshad number, check if [2010..2019] are primes.
Sum all valid primes, done.
This is actually a tree structure, solve it with BFS.