No you don’t see it in iCloud directly, but they synced to your other device. So you can try to export there. Maybe not the current data, 1-2 days behind for me. But worth a try.
The volume is obviously the issue with this. Fragmentation of the data into more manageable chunks seems like the most logical approach given hardware and OS limitations.
Workflow (app) can extract sub-sets of health data, but it would be a lot of work to export everything. If you just want a specific sub-set of data then maybe it would work for you.
The alternative to that would be a health app with granularity controls for exporting of health data. Not tried it myself, but maybe this one or one like it?
I’ve been using an app, QS Access. It is free! It exports a CSV file with columns for medical information you select. This keeps the size reasonable, but you can’t export a subset of dates.