Here is an essentially tautological answer. The notion of uniformity makes sense also for condensed sets -- it is a condensed set $X$ together with certain subsets $U\subset X\times X$ termed entourages satisfying all the usual axioms. Moreover, one can also define the completion of $X$ with respect to its uniform structure "by interpreting everything internally in condensed sets".
If $X$ is a condensed abelian group with a nonarchimedean uniformity -- meaning say that the $U$'s above can be chosen to be subgroups, and all $X/U$ are discrete (as condensed sets) -- then the completion of $X$ is the inverse limit of the $X/U$, and hence is solid.