Local interface effects modulate global charge order and optical properties of 1T-TaS$_2$/1H-WSe$_2$ heterostructures

1T-TaS$_2$ is a layered charge density wave (CDW) crystal exhibiting sharp phase transitions and associated resistance changes. These resistance steps could be exploited for information storage, underscoring the importance of controlling and tuning CDW states. Given the importance of out-of-plane interactions in 1T-TaS$_2$, modulating interlayer interactions by heterostructuring is a promising method for tailoring CDW phase transitions. In this work, we investigate the optical and electronic properties of heterostructures comprising 1T-TaS$_2$ and monolayer 1H-WSe$_2$. By systematically varying the thickness of 1T-TaS$_2$ and its azimuthal alignment with 1H-WSe$_2$, we find that intrinsic moiré strain and interfacial charge transfer introduce CDW disorder in 1T-TaS$_2$ and modify the CDW ordering temperature. Furthermore, our studies reveal that the interlayer alignment impacts the exciton dynamics in 1H-WSe$_2$, indicating that heterostructuring can concurrently tailor the electronic phases in 1T-TaS$_2$ and the optical properties of 1H-WSe$_2$. This work presents a promising approach for engineering optoelectronic behavior of heterostructures that integrate CDW materials and semiconductors.