Nuclei in the vicinity of driplines have been receiving a lot of attention in nuclear structure research. In the nuclei, the continuum coupling is crucial in reproducing weakly-bound or unbound properties. To calculate observables of the nuclei as open quantum systems, we have developed valence-space effective operators in the complex-momentum coordinates using many-body perturbation theory within the Gamow Hartree-Fock Berggren basis. Starting from initial two- and threenucleon forces from the chiral effective field theory, we have derived the Gamow-Teller \b{eta}-decay matrix elements for sd-shell nuclei. With both three-nucleon force and continuum coupling included, the Gamow shell-model calculation can properly reproduce experimental data. We find that the calculation can also well reproduce the \b{eta}-decay isospin asymmetry between the dripline nucleus 22Si and its mirror partner 22O, in which the s1/2 continuum plays a key role. The Thomas-Ehrman shift is visible in the mirror energy differences between the mirror daughters 22Al and 22F, and it can be explained by the continuum effect and three-nucleon force.