  There is a heated debate on the Josephson effect in twisted
Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ flakes. Recent experimental results suggest the
presence of either anomalously isotropic pairing or exotic $d$+i$d$-wave
pairing, in addition to the commonly believed $d$-wave one. Here, we address
this controversy by fabricating ultraclean junctions with uncompromised
crystalline quality and stoichiometry at the junction interfaces. In the
optimally doped regime, we obtain prominent Josephson coupling (2-4 mV) in
multiple junctions with the twist angle of 45$^\circ$, in sharp contrast to a
recent report that shows two orders of magnitude suppression around 45$^\circ$
from the value at 0$^\circ$. We further extend this study to the previously
unexplored overdoped regime and observe pronounced Josephson tunneling at
45$^\circ$ together with Josephson diode effect up to 50 K. Our work helps
establish the persistent presence of an isotropic pairing component across the
entire superconducting phase diagram.
