The phrase "is entwined" is correct and can be used in written English.
One possible example is: "The threads of their lives are so closely intertwined that it's hard to imagine one without the other." In this sentence, "is entwined" indicates a strong connection or intertwining between two people or things. Another example could be: "His love for music and poetry is entwined, with each inspiring the other." In this sentence, "is entwined" suggests a close relationship or connection between the two hobbies. Overall, "is entwined" is a great way to describe a strong or intertwined relationship between two people or things and can be used in a variety of contexts.
Dictionary
is entwined
verb
To twist or twine around something (or one another).
Exact(58)
That past is entwined with American history.
The history of Bay Hill is entwined with Woods' achievements.
For the Bachmanns, the issue is entwined with faith.
Like Steve Jobs's, his personality is entwined in his company's.
The creation of the Progressive Artists Group is entwined with that of independent India.
Whatever the quibbles might be, the rivalry is entwined with the World Cup.
Snakes twist up and around the largest proscenium, and another is entwined in thick vines.
But the fate of the middle class counties and urban ghettos is entwined.
That excellence is entwined with melancholy at the repeated abandonment of the old self.
The serpent is entwined, in surprisingly friendly fashion, around Adam's left arm.
That story is entwined with the story of my own childhood in Hong Kong," she said.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com