  The femtoscopic study of pairs of identical pions is particularly suited to
investigate the effective source function of particle emission, due to the
resulting Bose-Einstein correlation signal. In small collision systems at the
LHC, pp in particular, the majority of the pions are produced in resonance
decays, which significantly affect the profile and size of the source. In this
work, we explicitly model this effect in order to extract the primordial source
in pp collisions at $\sqrt{s} = 13$ TeV from charged $\pi$-$\pi$ correlations
measured by ALICE. We demonstrate that the assumption of a Gaussian primordial
source is compatible with the data and that the effective source, resulting
from modifications due to resonances, is approximately exponential, as found in
previous measurements at the LHC. The universality of hadron emission in pp
collisions is further investigated by applying the same methodology to
characterize the primordial source of K-p pairs. The size of the primordial
source is evaluated as a function of the transverse mass ($m_{\rm T}$) of the
pairs, leading to the observation of a common scaling for both $\pi$-$\pi$ and
K-p, suggesting a collective effect. Further, the present results are
compatible with the $m_{\rm T}$ scaling of the p-p and p$-\Lambda$ primordial
source measured by ALICE in high multiplicity pp collisions, providing
compelling evidence for the presence of a common emission source for all
hadrons in small collision systems at the LHC. This will allow the
determination of the source function for any hadron--hadron pairs with high
precision, granting access to the properties of the possible final-state
interaction among pairs of less abundantly produced hadrons, such as strange or
charmed particles.
