Multivariate power series are implemented by #1956.  As mentioned on that ticket, the existing code for PowerSeriesRing did not allow multivariate power series rings to be constructed using the same arguments as multivariate polynomials accept:
sage: T = PowerSeriesRing(QQ,3,'t'); T
Multivariate Power Series Ring in t0, t1, t2 over Rational Field
sage: T = PowerSeriesRing(QQ,'t',3); T
Power Series Ring in t over Rational Field
sage: T.default_prec()
3
sage: P = PolynomialRing(QQ,'t',3); P
Multivariate Polynomial Ring in t0, t1, t2 over Rational Field
 
There is a non-trivial body of code (elliptic curves, and maybe p-adics) which makes use of this syntax.
CC:  @nilesjohnson
Component: commutative algebra
Keywords: power series, deprecation warning
Issue created by migration from https://trac.sagemath.org/ticket/9980