Breaking the AGB Color Degeneracy with Variability and H$_2$O: A Consistent Picture of AGB Chemistry, Dust, and the J-Region Across Environments

Resolved asymptotic giant branch (AGB) populations present many observational puzzles. We consider three often treated separately: photometric C/O classification boundaries must be redrawn empirically in new environments; hydrostatic model grids are too blue in bands sampling H2O absorption; and J-region (JAGB) luminosities can differ between fields of a single galaxy. Pulsation connects them into a coherent picture. Using SPHEREx spectroscopy of AGB stars in the Large Magellanic Cloud (LMC) with JWST/NIRCam photometry and HST time-series of the SN Ia host M101, placed on a common scale by synthetic photometry, we investigate how AGB variability, surface chemistry, and circumstellar dust depend on environment. We develop an F182M index sensitive to 1.9$μ$m H2O absorption that chemically classifies variable AGB stars and reveals oxygen-rich (O-rich) stars degenerate with carbon-rich (C-rich) stars in broadband colors. Because these features arise in extended atmospheric layers, hydrostatic grids struggle to reproduce them. Pulsation and circumstellar dust are asymmetrically linked: nearly all stars with substantial infrared excess are variable, while many variables show little dust. This supports mass loss initiated by pulsation and enhanced by dust formation. Variable O-rich AGB stars in M101 are up to ~0.7 mag redder than their LMC counterparts in dust-sensitive colors, consistent with more efficient silicate-dust production at higher metallicity, while C-rich populations depend less on environment. Color windows that select C-rich stars cleanly in the LMC are therefore 33-68% O-rich in the metal-rich M101. This challenges the J-region's universality as a standard candle while evading standard self-consistency checks. We recommend combining variability, or the infrared excess that implies it, with photometry of molecular features to improve AGB classification at 0.75-5.0$μ$m.