Use std::any for DataIO context

[dschwen]

Closes #32302

[moosebuild]

Job Precheck, step Clang format on 10b9e50 wanted to post the following:

Your code requires style changes.

A patch was auto generated and copied here
You can directly apply the patch by running, in the top level of your repository:

curl -s https://mooseframework.inl.gov/docs/PRs/32303/clang_format/style.patch | git apply -v

Alternatively, with your repository up to date and in the top level of your repository:

git clang-format e4407b31a57ef5bd7bcb870595bbe7897b813978

[moosebuild]

Job Test, step Results summary on 2ee5605 wanted to post the following:

Framework test summary

Compared against e4407b3 in job civet.inl.gov/job/3542080.

No change

Modules test summary

Compared against e4407b3 in job civet.inl.gov/job/3542080.

No change

[moosebuild]

Job Documentation, step Docs: sync website on 2ee5605 wanted to post the following:

View the site here

This comment will be updated on new commits.

[loganharbour]

No concerns here. I've wanted this for a while. Now to fix...