Floating offshore wind is central to Korea's deep-water strategy, but installation choices remain poorly structured at the project-planning level. This paper proposes an installation compatibility framework that organises the selection problem along foundation type, water depth zone, and metocean severity. For each axis combination, the framework returns a feasibility verdict, an operability band, a method-maturity level, and dominant constraint codes. Applied to the Korean East Sea using GEBCO 2026 bathymetry, Korean ERA5 and hindcast data, and four installation methods (fully assembled wet tow, TLP integrated tow-and-tensioning, heavy-lift-vessel-based offshore turbine mating, and catamaran-based onsite installation), the framework yields a foundation-depth-severity compatibility matrix and maps the Ulsan floating project portfolio into it. The matrix shows that the practical installation choice space in Korea is much narrower than the conceptual design space: semi-submersible and barge wet tow form the only rows with Feasible verdicts and Proven maturity across their applicable depth ranges, while spar and TLP concepts remain structurally or logistically gated. The framework complements existing installation reviews and planning models as an installation-compatibility layer upstream of technoeconomic analysis, providing a structured basis for identifying hull-form, port, fleet, and validation investments needed to move currently Conditional foundation-method combinations into Feasible territory.