The question is not trivial, and to my knowledge the answer is not known: there is no known uniform upper bound for the $p$-adic valuation of $(p-1)!+1$ (although such a bound most probably exists, as you indicate).

The only result I know in this direction is that $(p-1)!+1$ is not a power of $p$ for any $p>5$, see e.g. [this link][1].

This does provide an upper bound for the $p$-adic valuation, although a very weak one. A natural problem would be to improve this bound, but a uniform upper bound may be out of reach given current technology.


  [1]: https://math.stackexchange.com/questions/805068/to-find-all-n-such-that-n-11-is-a-perfect-power-of-n