In a FPTP voting system, a vote for a third party will dilute the vote of the party closest-aligned to the preferences of the voter casting it- an effect that implicitly aids the party farthest-away from the voter’s preference. This means the winner doesn’t need a majority, they just need divided opponents.

In what way does addition to a third sum dilute the first two sums?

If Candidate A has one vote, Candidate B has one vote, and Candidate C has one vote, does adding one to Candidate C's sum somehow detract from Candidate A's sum?

Does it somehow give Candidate A an advantage over Candidate B, who still have equal and unchanged sums?

Of course not. That would violate basic math.

It's interesting, however, that you highlight a basic need for divided opponents as the con to a third party... yet it applies better to the current duopolistic nature where either party is increasingly dependent on nothing more than the polarized and divided voterbase. Look no further than continued blue no matter who etc. and ongoing painting of entire parties in a given light to the neglect of the actual candidates.

The existence of this spoiler effect in FPTP requires voters to vote based on how they bet other voters will vote, instead of signaling their actual preferences, in order to avoid dividing their support and throwing the election to the opposing side.

FPTP places no such requirement on voters - the only presence of such is your absurd insistence such a requirement exists.

Do you see this requirement in place in some form of legislation you must adhere to? No?

Ironically, if a voter signaled their actual preferences - to the disregard of blue no matter who and similar nonsense - it's likely third parties would be faring far better. Unfortunately, you and others here seem to be dead-set on vote shaming outside the duopoly.

This prevents the parties from knowing what voters really want

Oh? Canvassing has ceased to exist? The results of other elections - especially those in primaries where the primary differences are policy choices and messaging (to those policies) - can't serve as any form of indicator?

Interesting.

while giving donors and insiders massive leverage by way of giving them the ability to influence which candidates voters will bet ‘can win’

You once-more describe the current state of things while attempting to describe some other state of things.

It’s harmful to democracy, to the voters, and to the public interest, but it’s fantastic for party insiders and donors that want things the public doesn’t want.

The only harm here is your insistence a voter should vote how you believe they should vote to the neglect of their actual preferences - a thing that actually damages democracy.