Can one write poems that follows a rhyme scheme but no metre?

As a non-English speaker, I wonder if one can write English poems that follow a rhyme scheme but no metre?

If so, what is this form called? And can you kindly point out notable poets that practised this form?

Thanks in advance.

TLDR: Poets have definitely written poems like this. I would call them rhymed free verse. On one hand, for some definitions of free verse, this is a contradiction in terms. On the other hand, this kind of poem has been called free verse, and there does not seem to be another name for them.

Lexico defines free verse as:

Poetry that does not rhyme or have a regular meter.

So according to Lexico, rhymed free verse is a contradiction in terms.

On the other hand,

Merriam-Webster defines free verse as:

verse whose meter is irregular in some respect or whose rhythm is not metrical.

So according to this definition, rhymed free verse is possible.

There is a famous poem called Patterns by Amy Lowell. The first stanza is:

I walk down the garden paths,
And all the daffodils
Are blowing, and the bright blue squills.
I walk down the patterned garden paths
In my stiff, brocaded gown.
With my powdered hair and jewelled fan,
I too am a rare
Pattern. As I wander down
The garden paths.

Patterns certainly rhymes. Does it have meter? If it does, it's not a very regular one. It is often classified as free verse. And it was written by Amy Lowell, who wrote a lot of poems in free verse (only some of which rhyme).

Poetry doesn't require either rhyme or metre. A classic example is free verse.

From "An Introduction to Free Verse Poetry" by Jackie Craven:

Free verse poetry has no rhyme scheme and no fixed metrical pattern. Often echoing the cadences of natural speech, a free verse poem makes artistic use of sound, imagery, and a wide range of literary devices.

… Some free verse poems are so short, they might not resemble poems at all. In the early 20th century, a group who called themselves Imagists wrote spare poetry that focused on concrete images. The poets avoided abstract philosophies and obscure symbols. Sometimes they even abandoned punctuation. “The Red Wheelbarrow,” a 1923 poem by William Carlos Williams, is free verse in the Imagist tradition. In just sixteen words, Williams paints a precise picture, affirming the importance of small details:

so much depends
upon
a red wheel
barrow
glazed with rain
water
beside the white
chickens.

Other free verse poems succeed at expressing powerful emotions through run-on sentences, hyperbolic language, chanting rhythms, and rambling digressions. Perhaps the best example is Allen Ginsberg's 1956 poem "Howl." Written in the tradition of the Beat Movement of the 1950s, "Howl" is more than 2,900 words long and can be read as three strikingly lengthy run-on sentences.

Highly experimental poetry is also often written in free verse. The poet might focus on images or word sounds without regard to logic or syntax. Tender Buttons by Gertrude Stein (1874–1946) is a stream-of-consciousness collection of poetic fragments. Lines like "A little called anything shows shudders" have perplexed readers for decades. Stein's startling word arrangements invite debate, analysis, and discussions on the nature of language and perception. The book often prompts readers to ask, What is a poem?

And from Wikipedia:

Free verse is an open form of poetry, which in its modern form arose through the French vers libre form. It does not use consistent metre patterns, rhyme, or any musical pattern. It thus tends to follow the rhythm of natural speech.

In short, there are certainly genres of poetry that don't have to include any of the standard conventional structures that many people think of when they think of poetry.