'Opposites' are what Wittgenstein called a language-game. It is a conceptual metaphor, that we can use to organise experiences, towards making inferences.
Consider hot and cold. What is your reference? Body temperature right, 'luke warm'. So are the categories hotness and coldness, out there in the world being opposite to each other? No, they have an implicit context, they are tools we use, relationally to ourselves, to organise experiences and communicate about them. But we can go into our experiences more deeply, we can define temperature scales and so on.
Consider them as an example of 'chunking', like how we group similar experiences so that we can analyse probabilities: Does logic give us a single definitive and universal answer for comparing the odds of unlikely events?
The more general issue of how we get math and logic from the world and why they are useful: The Unreasonable Ineffectiveness of Mathematics in most sciences
And the thorny example of understanding antonyms, that is good vs evil: Does philosophy have a dark side? And the tricky question of 'nothing': How to explain nothingness in Consciousness theory of Tegmark
If life and death are antonyms, what is being in a persistent vegetative state, a coma with brain-stem death? Are conscious and unconscious opposites? A child was part of it's mothers body, joined by the umbilical cord, so does leaving descendents mean the matrilineal line isn't dead? Is there less-alive and more-alive?
Defining life is a whole topic, like temperature you can go from having two categories hot and cold, more deeply into experiences, using entropy or real-patterns to quantify things. But, you can't put a sharp line between life and non-life, and that shouldn't be surprising because we think life 'blurred' into existence emergently. Viruses pose a serious challenge, because although they are 'dead' molecules they perform replucation by 'hacking' living cells. Detailed issues discussed here: Are Life and Intelligence analogous?
"are there philosophical definitions in which Life and Death lie in a
compatible, synonymous relationship?"
Synonyms..? I don't really see what you mean. It's interesting to consider the Taiji of Daoism, more commonly known as the yin-yang. In this picture it is not only the positive presence of the structure of a cup, but the negative presence of the empty space in the structure, that makes it what it is, makes it useful. We tend to look at death as negation of lie, ignoring how it has enabled complexity, made space for change. See: Is Death a Feature or a Bug? In the Daoist picture life and death arise together, shape each other. Apoptosis, programmed cell-death, literally carves our body shape from a lump of cells, for instance seperating our fingers. It prevents us getting cancer (mostly). And death is always there, a kind of ground of being that arose with life. More on the Taiji: Philosophers or philosophical traditions that reject symbolic reasoning
'Oposites' aren't simply outvin the world, waiting for us to notice them. It's a metaphor that we twist and extend and play with creatively. It is a game we play. See 'Surfaces and Essences: Analogy as the Fuel and Fire of Thinking', by Hofstadter & Sander. Organising experiences to extract useful guidance how to act, is knowledge. Chunking helps us make models of the world that simplify things enough to run on our squishy hardware. It's not 'are life and death synonyms or antonyms?', it's what inferences can we draw if we imagine them one way, or the other. It's what happens if, we engage playfully with experiences, to draw out metaphors and models, to build strange-loops and tangled-hierarchies.