Generally, the term you're describing is called a term of endearment, or a way to affectionately refer to a person you hold dear. There are many of them, from shortened names (Bess for Elizabeth) to animals (bunny) or sweet things (honey, sugar) to adjectives (beautiful, gorgeous).

The most important person is more specific. Your criterion suggests there is only one who is above all others. If you're trying to find a companion term (pun intended), you have a few options:

Soulmate or soul mate, as mentioned by another answer, suggests an ideal fit between two people who connect not merely physically but soul-deep. Oxford English Dictionary, "soulmate, n.":

A person who shares a deep understanding or bond with another; esp. one ideally suited to another as a lover or spouse.

According to Merriam-Webster, Samuel Taylor Coleridge is said to have invented the word in an 1822 letter to a young lady, where he says:

To be happy in Marriage Life, nay … in order not to be miserable, you must have a Soul-mate as well as a House or a Yoke-mate…

If you could go for a phrase, the love of my life is a common collocation for someone most dear to someone else. Even beyond the Queen song, the phrase has had wide currency from the 19th century onward. For example, here is an excerpt from "Only A Flirtation." Salem Observer, vol. XL, no. 10, 8 Mar. 1862, p. 1, as found in ReadEx's America's Historical Newspapers database:

Day after day the love, the one love of my life, grew into my heart, absorbing me to the exclusion of all else.

Similar phrases extend back to Middle English, including lef lif (dear life) from the Middle English Sir Orfeo:

O lef liif, what is te,

That ever yete hast ben so stille

And now gredest wonder schille?

(O dear life, what is with you, who ever yet have been so calm, and now cry strangely shrill?)

Finally, English has a habit of borrowing terms of endearment from other languages. Ma chérie and mon amie both come from French; inamorata comes from Italian; there are many nonce uses based on users' language backgrounds. Lebensmensch is a coinage from the author Thomas Bernhard, and the book Thomas Bernhard by Gitta Honegger uses the word as-is when explaining it:

While Frau Stavianicek remained Auntie to the world, in his books Bernhard coined the term Lebensmensch for her importance in his life. A simple enough compound of "life" and "person," it conveys so much more than its idiomatic English equivalent, "companion," used and elaborated as "life support" by the British translator of Wittgenstein's Nephew. (p. 59)

Why not just use lebensmensch, treating the sentiment behind it as effectively untranslatable? You can also translate it literally, accepting that it's a metaphor, as life support or (as just suggested in a comment by AndrewL64) lifeline?