I could see an informal arrangement of "you go do your thing, I can enjoy nerding it out in the lab for a few decades" happening. Like, not officially abdicating the title, but giving him enough powers that the title is mainly ceremonial.
This would be the most palatable idea for Levnekh, where he quietly becomes Jornakhs secondary. However, i would like to emphasize that despite it being the most palatable it is
not what he wants, and i feel it would be a betrayal of how Necrons have been presented ever since dynasties were created, to have him personally consider abdication of non ceremonial power. Overlords as presented are near all megalomaniacal to a fault and he is no exception, believing everything within their spheres are theirs to do with as they please. From his perspective, he has ruled successfully for millennia and just now outmaneuvered the greatest Lords in his region of space. He's only now hitting his stride and the traditional reason for abdication (oncoming senility) he believes to be irrelevant to his immortal frame. Again, not saying that such a thing cant be prompted and is completely off the table, but it will almost certainly not be fully voluntary.
As to The Yulenoths Tendency towards techno-sorcery and the level of appeal becoming a full cryptek has. Levnekh, and the Yulenoth before them do not want to become full crypteks. Full crypteks, after all are barred from ruling territory. That said, having access to the skills of crypteks and being known to be friendly with them has their upsides, as you have already discovered. Being forced to become a cryptek full time for a scion of the Yulenoth would be comparable to religious minded Emperors in Byzantium being forced to become monks. They may have the skills and mindset for their new life but they will always long for the days that they held power. The emphasis after all is on the
Lords part of Scholar Lords
Finally, As to how Diplomacy can be used. There's in general relatively few thing that dynasties would jointly do either than strictly military, and i would be leaning on you guys creating any hypothetical deals. However an example could be that in exchange for a certain quantity of resources (which will be explained post time skip) you would be able to send a cryptek to construct a certain marvel for that specific dynasty. Likewise if you felt that you did not have a surfeit of capable generals for an upcoming war, you could request a famed martial dynasty eg the Aghrekun send one of theirs in exchange for what they considered fair. Joint infrastructure projects that are useful to both dynasties is also a possibility, such as building a "road" of cleared space between the two dynasties to facilitate easier travel. There are also certain technological specialties which many greater dynasties posses (The Thotk have famously bound radiation to their weapons which sickens all living creatures nearby) which could be traded, though they are cherished extremely highly, Teleportive construction being the main one you possess even if it not possessed exclusively by you.
This is by no means a complete list, and some dynasties will approach you for deals and information themselves. In terms of embassies, The greater the level of embassy would increase the likelihood of them giving you a favorable response as your people whisper endlessly in their ears about your greatness, power and wisdom.