Graphitic carbon nitride (g-C$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$N$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$) exhibits unique properties as a support for single-atom heterogeneous catalysts (SAHCs). Understanding how the synthesis method, carrier properties, and metal identity impact the isolation of metal centers is essential to guide their design. This study compares the effectiveness of direct and postsynthetic routes to prepare SAHCs by incorporating palladium, silver, iridium, platinum, or gold in g-C$\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}$N$\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ of distinct morphology (bulk, mesoporous and exfoliated). The speciation (single atoms, dimers, clusters, or nanoparticles), distribution, and oxidation state of the supported metals are characterized by multiple techniques including extensive use of aberration-corrected electron microscopy. SAHCs are most readily attained via direct approaches applying copolymerizable metal precursors and employing high surface area carriers. In contrast, although post-synthetic routes enable improved control over the metal loading, nanoparticle formation is more prevalent. Comparison of the carrier morphologies also points toward the involvement of defects in stabilizing single atoms. The distinct metal dispersions are rationalized by density functional theory and kinetic Monte Carlo simulations, highlighting the interplay between the adsorption energetics and diffusion kinetics. Evaluation in the continuous three-phase semihydrogenation of 1-hexyne identifies controlling the metal-carrier interaction and exposing the metal sites at the surface layer as key challenges in designing efficient SAHCs.