Is it possible, with Macros, to run a db query for a block-id an build the {{embed ((block-id))}} inside a page?

Macros don’t support Advanced Queries:

And you need Advanced Queries to retrieve a block’s ID.

But you could take another route and use a Simple Query:

{{query (and “search terms here” (sample 1))}}

It should be possible to define a macro with that and style it with CSS to make the result look like an embedded block.