>Imagine a version of English extended

You mean restrained. More specifically what you're proposing can formally be referred to as controlled natural language with executable semantics. Some attempts similar to this have been Attempto Controlled English and ClearTalk. (And Logos that someone showed here recently.)

>text would not just require reading; it would require executing algorithms embedded in the language itself

Arguably mathematics is just that.

>just like LaTeX for scientists

Future doesn't look very bright for LaTeX with Typst getting traction.