How do I make rows of views blocks on a basic page reacting collectively to an exposed filter?
Views Attachments Displays have the option to inherit the exposed and contextual filters from the Views displays they're attached to. So you can try to create one Views Page Display with some of your results, then create as many Attachment Displays (not Block Displays) as you need and attach them to the Page Display. 

I haven't tried the Layout Builder with different Views displays like that, but I think it may work to rearrange them a bit. 

I think you could also have Views Blocks (that are on the same Views) share the same Exposed filter settings (don't override them), and use the Exposed filter in a block option where you place the exposed filter part of Views as a block in a theme region instead of always appearing it automatically above the Views results. 

You may also want to check out the Views Global Filter module that affects all Views exposed filters once a user chooses one option.