How to do a two-sample z-test with <3 observations?

The accepted way to do z-tests in R seems to be the z.test function from BSDA package. However, it doesn't seem to work with less than 3 observations. This is confusing to me, because the z-test shouldn't require more than one observation. It shouldn't use the sample to estimate the variance - it should use the inputted sigma.

Am I doing something wrong? Is there a better way to do z-tests in R?

Here you can see the z-test succeed with 3 observations in each group and fail with 1.

library(BSDA)
  
s <- 0.2
x <- c(1, 1.5, 1)
y <- c(2, 2.5, 2)
z.test(x, y, sigma.x = s, sigma.y = s)
#> 
#>  Two-sample z-Test
#> 
#> data:  x and y
#> z = -6.1237, p-value = 9.141e-10
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#>  -1.3200608 -0.6799392
#> sample estimates:
#> mean of x mean of y 
#>  1.166667  2.166667
x <- 1
y <- 2
z.test(x, y, sigma.x = s, sigma.y = s)
#> Error in z.test(x, y, sigma.x = s, sigma.y = s): not enough x observations

^{Created on 2023-06-27 with reprex v2.0.2}

I agree with the commenters that there doesn't seem to be any good reason that BSDA::z.test can't handle a two-sample Z test with an n (per group) of 1.

I looked around with library(sos); findFn("z test") and found misty::test.z, but that also seems to have issues.

However, the PASWR package (which has the same maintainer as BSDA !) appears to work OK:

PASWR::z.test(x, y, sigma.x = s, sigma.y = s)
	Two Sample z-test
data:  x and y
z = -3.5355, p-value = 0.000407
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -1.5543615 -0.4456385
sample estimates:
mean of x mean of y 
        1         2 

The p-value agrees with the direct calculation:

2*pnorm(abs(x-y)/sqrt(s^2+s^2), lower.tail = FALSE)