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Warning: this "answer" is not providing a workaround, just digging into the error.

First, a comment, you can call QQbar instead of QQ.algebraic_closure(), and there is a shortcut for creating your polynomial ring R:

sage: R.<x> = QQbar[]
sage: R
Univariate Polynomial Ring in x over Algebraic Field

Now, let us define the ideal and explore the functionality around is_prime.

sage: I = Ideal([x^2+2])
sage: I
Principal ideal (x^2 + 2) of Univariate Polynomial Ring in x over Algebraic Field
sage: I.is_prime()
False

Changing to a multivariate polynomial ring:

sage: S.<x,y> = QQbar[]
sage: S
sage: J = Ideal([x^2+2])

The error is triggered by

sage: J.is_prime()
...
TypeError: Cannot call Singular function 'primdecSY' with ring parameter of type '<class 'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain_with_category'>'

The documentation of the is_prime method that applies to the ideal J is available by

sage: J.is_prime?

and the source code by:

sage: J.is_prime??

There we discover that is_prime is really trying to compute the decomposition of J into prime ideals using the method complete_primary_decomposition and checking this decomposition against J.

If we try that method, we see that this is where the failure is happening:

sage: J.complete_primary_decomposition()
...
TypeError: Cannot call Singular function 'primdecSY' with ring parameter of type '<class 'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain_with_category'>'

We can get the documentation and source code for the method:

sage: J.complete_primary_decomposition?
sage: J.complete_primary_decomposition??

and we see that after trying to return J.__complete_primary_decomposition[algorithm='sy'], which fails raising an AttributeError, the method goes on and imports sage.libs.singular and then defines primdecSY as sage.libs.singular.ff.primdec__lib.primdecSY and P as primdecSY(J). Let's try that:

sage: primdecSY = sage.libs.singular.ff.primdec__lib.primdecSY
sage: primdecSY
primdecSY (singular function)
sage: P = primdecSY(self)
...
TypeError: Cannot call Singular function 'primdecSY' with ring parameter of type '<class 'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_domain_with_category'>'

So here is our TypeError.

If we want to read more about where this error is triggered:

sage: sage.libs.singular.ff.primdec__lib.primdecSY?

That's all I have, now we need someone with more expertise to tell us why Sage is having trouble calling primdecSY with our polynomial ring in several variables over QQbar as a parameter.