How to generate, inherit and modify options to Dataset in Version 12.1

Questions
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1

Here’s a notebook that explains the problem:

Open in Wolfram Cloud ↗
2

Changing a Dataset’s options works analogously to Image. You wrap the dataset with Dataset[…, options]:

Dataset[q, ItemDisplayFunction -> (Round[#, 0.01] &)]

Preserving Dataset options through Dataset operations is on the development agenda.