What is the word for two or more people realise that something is happening but when no one will openly express it? A competition or problem, perhaps

"...and I immediately feel defeated in the undeclared competition for bodily supremacy."

• undeclared - not announced or openly acknowledged : not stated or decided in an official way : not declared, an undeclared war. (MW)

• "There was an undeclared competition among us."
• "I also remember an undeclared competition among the students."

You may not get closer than palpable.

From Vocabulary.com (amended):

palpable [adjective]

The prototypical meaning is that when something is palpable, you can touch or handle it. However, the word is often used to describe things that usually can't be handled or touched, such as emotions or sensations.

You probably won't see palpable used to describe, say, an egg or a doorknob or a motorcycle. Palpable is usually reserved for situations in which something invisible becomes so intense that it feels as though it has substance or weight. Someone who has experienced a death in the family might say that her grief feels palpable.

Thus

... I immediately feel defeated in the palpable fight/struggle for bodily supremacy.

Tacit would suggest something unspoken but inferred or implied in the situation. Oxford English Dictionary, "tacit, adj.":

2. Not openly expressed or stated, but implied; understood, inferred.

That has the benefit of suggesting something both not openly expressed and understood or felt by the participants.

Even on days where I feel particularly confident with myself, I scroll on social media to see my classmates looking so beautiful and skinny in bikinis, no roll or stretch marks in sight, and I immediately feel defeated in the tacit fight for bodily supremacy.

You presumably discounted unacknowledged. Starting from your suggestion that the competition is not acknowledged, there is a range of words that may fit the specification. Here are a couple of other un-... words:

undeclared = Not publicly announced, admitted, or acknowledged

Oxford Lexico

unspoken = not stated, although thought, understood, or felt

Cambridge Dictionary

and here are two other possibilities:

tacit = understood without being expressed directly

Cambridge Dictionary

latent = present and capable of emerging or developing but not now visible, obvious, active

Merriam Webstre

To me, latent and undeclared have slight feelings of a possible future admission of the competition. I feel unstated and tacit are nice because they relate more strongly to the mute understanding of the presence of the competition.