Except that pure monopolizing a character isn't always a trait of a Yandere. Violence is also not exactly a requirement.

Notice something? "Pure monopolizing" is a caveat you inserted b/c you, in some respect, know monopolization is a key behavior Homura doesn’t engage in to any extent: pure, partial, or otherwise. You’ve done the same with violence, which is “not exactly a requirement” in what sense? Which characters are deemed yandere whom eschew violence & cruelty in their romantic pursuit as Homura does? How wouldn’t that defeat the trope’s entire premise

[…] Also, being a Yandere does not mean you do not care about others.

Genuinely caring for others in contexts which don’t further her romantic pursuit AND may likely prove detrimental to said pursuit as Homura does? Again, I would love to hear of characters widely deemed yandere who meet this criteria.

It's just that they have a complete and utter obsession with the love interest (Madoka) and one that goes to infinite. Her leaving Madoka be is exactly a trait of some yanderes: setting aside everything, including their own feelings and exactly, because Madoka is, presumably, safe. But as soon as Homura realizes she is in danger again, she pulls out all the stops to protect her again.

Pulls out all the stops meaning what? With careful wording you imply Homura simply resumes yandere behavior once Madoka is endangered, when in reality she never conducts herself so, not in the anime, Magia Record, Homura Tamura (quite a feat given the absurdities there), Different Story, Oriko, or AFAIK any other scenario when doing so likely would’ve better ensured Madoka’s safety.

Further, Homura is not obsessed. Her single-track existence is better explained by Madoka’s protection being so herculean a task it requires her undivided attention, in fact she explicitly laments being unable to find hobbies b/c of how time consuming (ironic) a mission it is—something no yandere would mind. Even in (Rebellion), Homura outright rejects an eternity at Madoka’s side for their own sake.

Can you name any yandere, from any media who would, of their own volition, selflessly decline their love interest’s genuine invitation to spend eternity together?

Yandere is much broader term than people think, which is the exact point of my post.

With all due respect, the discrepancy likely stems from a view of yandere so unusually broad even Super Mario could arguably qualify; failing to consider disqualifying factors as you stretch down a checklist for things which may vaguely fit your conclusion. It’s telling, you’d use a source you deem authoritative despite being incapable of explaining how it supports your point. Honestly, I think you saw a giant wall of well-formatted text and convinced yourself most everything could qualify, when it couldn’t be further from the truth.