Error: Mishandles input errors
When fgets() returns NULL due to input error, this function might return 0 (for EOF).
Lack of in code documentation
A declaration like int fgets_line(char **line, size_t *capacity, size_t *length, FILE *stream); deserves to exist with documentation describing the goals and functions limitations. (e.g. a .h file.) Do not assume users want to dissect the function source code.
Minimum work
"minimal work as possible" --> User I/O is a sink-hole of time. A linear extra call to strlen() will not be noticed.
Pedantic: Reliance on not reading a null character
Code performs incorrectly with *length = position - *line + strlen(position); should fgets() read a null character.
Either adjust code to detect reading a null character (not easy) or consider dropping the length parameter. Calling code can use strlen().
Pedantic: *capacity not validated
If fgets_line() called with a wee *capacity (like 0 or 1), (*line)[various] risks accessing the array out of bounds. Take care in assuming what how the caller set up the buffer pointer and size. It may have been right-sized after a prior read.
Pedantic: Out of int range
fgets() uses an int for the size, so *line + *capacity - position risks out-of-range conversion.
Design
I am not a fan of giving the user the ability to overwhelm memory resources and prefer a sane upper bound to allocation size.