Is there a nontrivial way to consider products of archimedean and non-archimedean spaces in the context of Clausen–Scholze's analytic geometry?

Context: Last week during a conference in Essen (School on Arithmetic Geometry) Peter Scholze has given a talk about his (joint with Dustin Clausen) work on analytic geometry. One of the main conceptual achievements of this theory is to provide a single framework encompassing both nonarchimedean geometry and complex-analytic geometry, using the theory of *solid* and *liquid* analytic ring structures, respectively.

After the talk one of the participants has asked whether there is a way in this theory to take a product of spaces living in those two worlds, one nonarchimedean (over some $\mathbb Z_p$) and one archimedean (over $\mathbb R$). The obvious answer, as explained by prof. Scholze, is that yes, you can take such a product, but it will be empty. This makes some sense — it is justified for instance by the fact that the solid tensor product $\mathbb Z_p\otimes^\blacksquare\mathbb R$ is zero (see Example 6.4 Scholze (joint with Clausen) - Lectures on condensed mathematics) (one may object using solid tensor product when involving $\mathbb R$, but let me just mention that a similar obstruction occurs when trying to consider product of objects over $\mathbb Z_p,\mathbb Z_q$ for $p\neq q$).

However, spaces of this flavor do appear, even within arithmetic geometry — the most standard examples are various adelic spaces appearing e.g. when defining Shimura varieties, which are (restricted) products of spaces over local fields. (Note: a natural suggestion would be to just put some analytic ring structure on the ring of adeles, but I don't believe it would give us the "right" geometric spaces we care about, see comments.)

Another example (which also appeared in that conference, and I'm tempted to believe is the one that prompted the question) is the product of a (Drinfeld) $p$-adic upper half plane with complex upper half plane, as it admits a discrete action of a group $\mathrm{SL}_2(\mathbb Z[\frac{1}{p}])$.

Given the "unifying" nature of condensed mathematics and analytic geometry, I would expect this framework to be able to accommodate such spaces. The regular ("non-completed") tensor product $\mathbb Z_p\otimes\mathbb R$ is still nontrivial over condensed group, so one could still hope that there is some way to produce analytic ring structures to accommodate those. Any ideas in that direction would be appreciated.

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