Add Integration Tests for downstream packages

[nickrobinson251]

Such as InlineStrings.jl, CSV.jl, ...

To avoid issues like #133

We could use a GitHub Action workflow like https://github.com/JuliaDiff/ChainRulesCore.jl/blob/v1.15.6/.github/workflows/IntegrationTest.yml

[quinnj]

Hmmmm.....maybe. I think we should make the Parsers interfaces much more well-defined and strict/robust, which is a big part of the aim in #127; I think if we have more solid user-facing overload functions, we avoid lots of scenarios where we accidentally break things by doing little tweaks.

But if it's not too much overhead/burden, I'm not opposed to doing downstream tests.

[quinnj]

Added by @nickrobinson251 in #137; thanks!