it's present perfect tense, is it not? (at least the english is... I just don't know how to do latin verbs)
or at least ... is it fair to say that this "have undertaken" part in latin is NOT in the (simple) past tense?
It's in perfect tense. The perfect tense in Latin might be translated in two ways: the past simple ("I did") or the present completed ("I have done").
Principal parts of suscipio (third conjugation of verbs ending with "io"):
The perfect tense is formed by using the third principal part with "i" dropped. Then add:
1st person, single: -i
2nd person, single: -isti
3rd person, single: -it
1st person, plural: -imus
2nd person, plural: -istis
3rd person, plural: -erunt (or -ere)
Thus, the perfect tense for third person plural can be either "susceperunt" or "suscepere".