  The idea of composite dark energy (DE) is quite natural since on general
grounds we expect that the vacuum energy (associated to the cosmological term
$\Lambda$) may appear in combination with other effective forms of DE, denoted
$X$. This was indeed the old proposal from 2006 (cf. Ref. [42]), called the
`$\Lambda$XCDM model'. In the current work, we deal with a simplified version
of this model and exploit the possibility that $X$ behaves as `phantom matter'
(PM), which appears in stringy versions of the running vacuum model (RVM).
Unlike phantom DE, it satisfies the strong energy condition like usual matter,
hence bringing to bear positive pressure at the expense of negative energy.
Bubbles of PM may appear in the manner of a transitory `phantom vacuum'
tunneled into the late universe before it heads towards a new de Sitter era,
thereby offering a crop field for the growing of structures earlier than
expected. Using SNIa, cosmic chronometers, transversal BAO, LSS data and the
full CMB likelihood from Planck 2018, we find that the tensions virtually
disappear in this stringy RVM scenario characterized by axionic dark matter.
The value of $H_0$ emerging from our analysis proves compatible with SH0ES to
within less than $0.25\sigma$ and the LSS growth tension is nonexistent. The
statistical information criteria point to very strong evidence in favor of the
PM solution. Finally, our approach favors quintessence-like behavior of the DE
below $z\simeq 1.5$ at $\gtrsim 3\sigma$ CL, which is compatible with the
recent DESI measurements.
