'budget of' is a correct usage of English in written form.
You can use it to express a specified amount of money allocated to pay for something. Example: The government has allocated a budget of $50 million to raise the standard of public healthcare.
Exact(60)
And all on a budget of £250.
The military budget of the US.
It enjoys an annual budget of $75m.
The budget of the first Rocky film.
The department enjoys a budget of £6m.
It is also a budget of stagnation.
There I had a budget of $66m.
$9bn is the budget of DPKO.
It currently has a budget of £253m.
That's considerably more than the annual budget of today's NHS.
"We still had got a budget of $200 million".
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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