First-Law Entropy and a Degenerate Extremal Remnant in a Minimal-Length Simpson--Visser-Type Regular Black Hole: Geometrothermodynamics, Phase Structure, and Observational Discriminants

We construct the first-law-consistent entropy of a geometrically minimal-length-deformed Schwarzschild spacetime, obtained via the areal-radius substitution $R(r)=\sqrt{r^{2}+\ell^{2}}$ on $r\in[0,+\infty)$ with $f(R)=1-2M/R$, whose nonvanishing Einstein tensor sources an effective geometric fluid w