pandoc-crossref must match the pandoc version, and also only the 3.10.0 release works on OSX Big Sur. Thus, it is not possible to get pandoc and pandoc-crossref running in a conda environment from the official channel or from conda-forge.
I could easily download the matching binaries from https://github.com/lierdakil/pandoc-crossref/releases/tag/v0.3.10.0 and copy them e.g. to the binpath:
$ which pandoc-crossref
/usr/local/bin/pandoc-crossref
$ curl -OL https://github.com/lierdakil/pandoc-crossref/releases/download/v0.3.10.0/pandoc-crossref-macOS.tar.xz
$ tar -xzvf pandoc-crossref-macOS.tar.xz
$ mv pandoc-crossref /usr/local/bin/pandoc-crossref
But I think that is not a clean approach, because conda will not know that I updated the version for pandoc-crossref.
What is a clean approach for updating a package managed by conda from a binary available on Github?
I updated it on the Conda Forge feedstock, which is what I regard as the "cleanest" solution.
How does one do that? First, OP had posted a comment on the feedstock in the PR that they wanted merged. This was the appropriate first step and hopefully in future cases that should be sufficient to prompt maintainers to act. In this case, it was not sufficient. So, as a follow up, I chatted on the Conda Forge Gitter to point out that the feedstock had gone stale and had non-responding maintainer(s). One of the core Conda Forge members suggested I make a PR bumping the version and adding myself as maintainer, and they merged it for me. In all, this took about 10 mins of work and ~2 hours from start to having an updated package on Anaconda Cloud.
Otherwise, there isn't really a clean solution for non-Python packages outside of building a Conda package. That is, clone the feedstock or write a new recipe, modify it to build from the GitHub reference, then install that build into your environment. It may also be worth uploading to an Anaconda Cloud user account, so there is some non-local reference for it.
In the special case that it is a Python package, one could dump the environment to YAML, edit to install the package through pip, then recreate the environment.