When the expected lifespan is over 400 years old, I don't think spending less than 10% of her life building the connections and life experiences that will help her be a successful heir is excessive.
Also, spending 5 years allows for significant experience and growth in both relationships with other people, and in developing skills. I figure 5 years apprenticeship in the Artisan guild is actually a pretty short time investment for the possible gains.
10 years to get a doctorate is normal. Do you think people that spent over 10% of their lifetime attending college made an extreme choice?
She can spend time building connections in ways that don't involve spending five years on each planet. And not all of the planets have equal value in terms of time spent there anyways - she should visit all of them, yes, but extended stays on all of them won't necessarily be beneficial.
Niflheim is weird as hell, and the people there make other actively uncomfortable. Five years there won't likely benefit Syr all that much, and may really be detrimental. Further, in other cases we shouldn't presume things - Syr being made an apprentice Artisan seems like it might actually be unlikely, as five years isn't likely enough time for her to actually become proficient enough to go beyond apprentice and it may well be the case that apprentices are chosen at much younger than 18 and I doubt they just open the opportunity to people who ask considering they have secrets that they keep.
On the other hand going to a college equivalent at Muspelheim would likely be beneficial. After that she could be brought back and go through the Officer's Academy or the Naval Academy. Then send her to Asgard for a few years to run our fief there for a while (and not necessarily with specific instructions - it could be interesting just to let her have free reign and see what she does with it, because when she becomes Planetary Governor of Avernus she's not going to have someone giving her orders). Then bring her back and have her go through the other Academy she hasn't done. And then perhaps have her work under Klovis-Ultan and help with the Diplomacy stuff for a while. Or maybe she'll want to join the Imperial Navy at some point with the goal of becoming an Admiral.
We should definitely ask her what her opinion is when the time comes, though, as we shouldn't attempt to run her life. NPCs do have agency.
EDIT: Remember that we are starting 5 year turns, so it's only 8 turns.
The actual turn length doesn't matter so much to me because in character Syr is still experiencing things in real time.