  Via the relative fundamental exact sequence of $p$-adic Hodge theory, we
determine the geometric $p$-adic pro-\'etale cohomology of the Drinfeld
symmetric spaces defined over a $p$-adic field, thus giving an alternative
proof of a theorem of Colmez-Dospinescu-Niziol. Along the way, we describe, in
terms of differential forms, the geometric pro-\'etale cohomology of the
positive de Rham period sheaf on any connected, paracompact, smooth
rigid-analytic variety over a $p$-adic field, and we do it with coefficients. A
key new ingredient is the condensed mathematics recently developed by
Clausen-Scholze.
