Google-sheets – What function can I use to conditionally format text depending on cursor position or active cell

You don't need a script for that; the built-in conditional formatting tools are flexible enough. Assuming the first row is for headers, apply conditional formatting to the range A2:A, with custom formula =len(join("", B2:Z2)). This means: join the content of cells, and find its length; the formatting applies if the length is greater than 0.

Replace Z by AZ or something else if you have more columns. (The formula will automatically adjust if you insert more columns between A and Z later.)

Bold formatting is found in the formatting dropdown, select "Custom" as below.

You cannot use the formatting of a cell as input to a formula.

But, it is easy to extend the range of conditional formatting so that it applies to A as well as to B, while being based on the data from B.

For example, formatting the range A2:B according to the custom formula =LEN($B2) colors both A and B if the column B cell is nonempty.

More generally, if the column references in your conditional formatting formula are absolute (like $B above), the result will be the same for all cells within the same row within the formatted range.