  We perform a global effective-field-theory analysis to assess the combined
precision on Higgs couplings, triple gauge-boson couplings, and top-quark
couplings, at future circular $e^+e^-$ colliders, with a focus on runs below
the $t\bar t$ production threshold. Deviations in the top-quark sector entering
as one-loop corrections are consistently taken into account in Higgs and
diboson processes. We find that future lepton colliders running at
center-of-mass energies below the $t\bar t$ production threshold can still
provide useful information on top-quark couplings, by measuring virtual
top-quark effects. With rate and differential measurements, the indirect
individual sensitivity achievable is better than at the high-luminosity LHC.
However, strong correlations between the extracted top-quark and Higgs
couplings are also present and lead to much weaker global constraints on
top-quark couplings. This implies that a direct probe of top-quark couplings
above the $t\bar t$ production threshold is helpful also for the determination
of Higgs and triple-gauge-boson couplings. In addition, we find that below the
$e^+e^-\to t\bar th$ production threshold, the top-quark Yukawa coupling can be
determined by its loop corrections to all Higgs production and decay channels.
Degeneracy with the $ggh$ coupling can be resolved, and even a global limit is
competitive with the prospects of a linear collider above the threshold. This
provides an additional means of determining the top-quark Yukawa coupling
indirectly at lepton colliders.
