A higher-power supercongruence for a truncated hypergeometric series

Let $p>3$ be a prime, and let $r$ be a positive integer. The supercongruence. First,

$$\sum_{k=0}^{p-1}(2pk+2k+1)\frac{\left(\frac{1}{p+1}\right)_k^{2p+2}}{k!^{2p+2}}\equiv 0\pmod{p^7}.$$

More generally,

$$\sum_{k=0}^{p^r-1}\left(2k\frac{p^{r+1}-1}{p^r-1}+1\right)\frac{\left(\frac{p^r-1}{p^{r+1}-1}\right)_k^{2\frac{p^{r+1}-1}{p-1}}}{k!^{2\frac{p^{r+1}-1}{p-1}}}\equiv 0\pmod{p^{2r+5}}.$$

This conjecture concerns supercongruences modulo high prime powers and generalizes the displayed case; its status is conjectural.