Strain and twist angle driven electronic structure evolution in twisted bilayer graphene

In twisted bilayer graphene (TBG) devices, local strains frequently coexist and intertwine with the twist-angle-dependent moir\'e superlattice, significantly influencing the electronic properties of TBG, yet their combined effects remain incompletely understood. Here, using low-temperature scanning tunneling microscopy, we study a TBG device exhibiting both a continuous twist-angle gradient from 0.35{\deg} to 1.30{\deg} and spatially varying strain fields, spanning the first (1.1{\deg}), second (0.5{\deg}) and third (0.3{\deg}) magic angles. We visualize the evolution of flat and remote bands in energy and real space with atomic resolution. Near the first magic angle, we discover an anomalous spectral weight transfer between the two flat band peaks, signifying the role of strain and electronic correlations, as further evidenced by an unusual spatial dispersion of these peaks within a moir\'e unit cell. In contrast, remote band peak energy offers a strain-insensitive indicator of the local twist angle. Structural analysis further reveals non-negligible shear strain across the sample. All observations are quantitatively reproduced by a continuum model that incorporates heterostrain and a self-consistent Hartree potential, revealing the critical but unexplored role of shear strain in shaping the low-energy electronic landscape of TBG.