UOCS. XVI. Census of post mass-transfer binaries across various evolutionary phases in M67

M67 is a well-studied solar-metallicity old open cluster that hosts a diverse set of exotic stellar populations that formed via mass transfer (MT). While case A, B, and C MT systems have been individually examined in several clusters, a comprehensive investigation of all MT types in different evolutionary stages within a single cluster remains limited. We detect post-MT systems using two different methods and thereby obtain a holistic view of the binary evolution and MT mechanisms prevalent in M67. We constructed spectral energy distributions for 141 UV-detected stars in M67 using far-UV data from AstroSat/UVIT, combined with archival data from Swift/UVOT, GALEX, Gaia, 2MASS, WISE, and other sources. Furthermore, we performed a detailed chemical abundance analysis of cluster members using high-resolution spectroscopy from the GALAH DR3+ survey. We identified 11 new main-sequence (MS) + white dwarf (WD) binaries with previously undetected hotter companions, effectively doubling the known MS+WD binary population in M67. This includes five confirmed extremely low-mass WDs with orbital periods <100–200 days and no chemical peculiarities, confirming case A or B post-MT systems. We also detected 13 long-period (>1000 days) single-lined spectroscopic binaries with enhancements in s-process elements (Ba, La, and Y), indicating case C post-MT systems enriched by thermally pulsing asymptotic giant branch companions that have evolved into undetected WDs. We demonstrate that M67 hosts a diverse population of post-MT binaries formed via case A, B, and C mechanisms. The unified view makes M67 a key benchmark for studying binary star evolution and highlights the role of UV observations and high-resolution spectroscopy in uncovering hidden stellar histories.