An optimized metastructure (MS) switchable between ultra-wideband (UWB) angle-insensitive absorption, and transmissive linear-to-circular (LTC) polarization conversion (PC), is proposed, which is a theoretical study. The structural parameters of this MS are optimized by the thermal exchange optimization algorithm. By modulating the chemical potential (μc) of the graphene-based hyperbolic metamaterial embedded in the MS, the MS can achieve UWB absorption in the absorption state and LTC PC in the transmission state. At normal incidence, in the absorption state, the MS exhibits absorptivity exceeding 0.9 within 7-15.45 THz, with a relative bandwidth (RBW) of 75.28%. By elevating μc, an UWB LTC PC is realized, with a RBW of 118.8%, achieving transmittance above 0.9 and the axial ratio below 3 dB. When prioritizing the angular stability, in the absorption state, the MS secures the angular stability of 75° for TE waves and 65° for TM ones. In the transmission state, the angular stability of PC reaches 60°, with RBW = 100.7%. Moreover, by manipulating μc, the tunability of UWB absorption is realized. The optimized MS provides a reference for designing multifunctional intelligent terahertz modulators, with promising application potential in domains like electromagnetic shielding, communication systems, and THz modulation.