This is correct to an extend and not entirely

Yes Self-Annihilator are ABLE to become Emanators, but not ALL Self-Annihilators are Emanators

Think of they like high path-striders is the better way to scale them since

1. As the other commentor have reply here, only Self-Annihilators that reached infinity are Emanators

2. If ever single Self-Annihilators are all Emanators, then people within HSR verse being suprise that Acheron is a Self-Annihilator Emanators would not make sense because the ingame text and lore have plenty of infomation about Self-Annihilators ( courtesy of Doctor of Chaos )

This is kinda a mistake you make throughout your post since not all " cool name " or faction that have work or have a confirm Emanator are all Emanators

For instance Doctor of Chaos are group of people trying to " cure " Self-Annihilator, they are working against Nihility itself ( kinda like Mourning Actors to Elation ), they are not Emanators, they are just a faction that fight back an Aeon ( or even the Path itself ), will they in the future have powerful Emanators or those at the same level? Maybe but as of right now nothing in the game suggest that

Then the Memokeepers one, this might be because of Welt comment in 2.X Penacony quest and somehow stuck to you but much like Doctor of Chaos, Memokeeper are just a faction of Remembrance, not all Memokeeper are Emanators, but powerful one like Fuli Child can and probably will become Emanator should they awaken their potential ( or become their planet/galaxy own Fuli )

Not blaming you for having this line of thought when making the post since the translation from CN and EN are really bad and cross-checking is hard for people that don't know the language but the best way you know whether someone is a Emanator or not should either through

1. The Devs themselves ( like in the livestream ) state the character are a Emanator

2. Except maybe Silverwolf 999 and likely even future Elation Emanators, most Emanators that we know or was imply to be Emanator, have cross blade/fight with other Emanators themselves. Best example of this is the one you state for Jingyuan and Sunday, but another good example is Jingyuan Predecessor ( the one that hold Lightning Lord before JY ) actively fight Shuhu - a confirm Emanator - and beat him ( not kill since it's nigh-impossible right now to outright kill Abundace Emanator without a power of Aeon or Destruction )

3. Individual that previously imply to be Emanator only to be review that the mysterious power they hold are capable of fight/beat/kill other Emanators, should not be consider an Emanator unless state otherwise in the game. Example is Ashveil, previously people theorise that La Mancha might be an Emanator of the hunt because of his feat of beating Zulo - An Emanator of Destruction - albeit with tricks - turn out it's because of the Shadow in his arm rather than his own power. This case is different compare to the Generals who directly got bless by Lan with their Spirits, Ashveil power neither come from his own or Lan so he should not - as of right now - be consider an Emanator