In this work, we use the {sc astraeus} (seminumerical rAdiative tranSfer coupling of galaxy formaTion and Reionization in N-body dArk mattEr simUlationS) framework which couples galaxy formation and reionization in the first billion years. Exploring a number of models for reionization feedback and the escape fraction of ionizing radiation from the galactic environment ($f_mathrm{esc}$), we quantify how the contribution of star-forming galaxies {(with halo masses $M_h>10^{8.2}$M$_odot$)} to reionization depends on the radiative feedback model, $f_mathrm{esc}$, and the environmental over-density. Our key findings are: (i) for constant $f_mathrm{esc}$ models, intermediate-mass galaxies (with halo masses of $M_hsimeq10^{9-11}$M$_odot$ and absolute UV magnitudes of $M_{UV} sim -15$ to $-20$) in intermediate-density regions drive reionization; (ii) scenarios where $f_mathrm{esc}$ increases with decreasing halo mass shift the galaxy population driving reionization to lower-mass galaxies ($M_hlesssim10^{9.5}$M$_odot$) with lower luminosities ($M_{UV} gtrsim-16$) and over-densities; (iii) reionization imprints its topology on the ionizing emissivity of low-mass galaxies ($M_hlesssim10^{9}$M$_odot$) through radiative feedback. Low-mass galaxies experience a stronger suppression of star formation by radiative feedback and show lower ionizing emissivities in over-dense regions; (iv) a change in $f_mathrm{esc}$ with galaxy properties has the largest impact on the sources of reionization and their detectability, with the radiative feedback strength and environmental over-density playing a sub-dominant role; (v) JWST-surveys (with a limiting magnitude of $M_{UV} = -16$) will be able to detect the galaxies providing $sim 60-70%$ ($sim 10%$) of reionization photons at $z=7$ for constant $f_mathrm{esc}$ models (scenarios where $f_mathrm{esc}$ increases with decreasing halo mass).