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I’m not quite sure what kind of scenario you’re asking for - e.g. there isn’t a way on the website to batch edit your identifications on other people’s observations. If you want to batch edit your own observations, hover over your profile pic in the top right of the header and choose “Edit Observations”, then filter it to your search interest, and “Batch edit”.
The example you referenced “works” in the context of the Identify page, which defaults to Needs ID/unreviewed obs, but I changed it to use Explore instead, which might reduce confusion. https://www.inaturalist.org/pages/search+urls#obs-id
Yes, this is what I’ve been doing, and a friend of mine used (I think) your basic idea on another thread relating to creating custom field guides to do a type of html mail merge of downloaded image urls to put them on his wordpress site, but it seemed logical in my optimistic little head that there’d be a way to sort by a field.