You don't need the tildes (~). See example below with data from the survey package:
library(survey)
#> Loading required package: grid
#> Loading required package: Matrix
#> Loading required package: survival
#>
#> Attaching package: 'survey'
#> The following object is masked from 'package:graphics':
#>
#> dotchart
library(srvyr)
#>
#> Attaching package: 'srvyr'
#> The following object is masked from 'package:stats':
#>
#> filter
data(api)
dclus1 <- apiclus1 %>%
as_survey_design(ids=dnum, weights = pw, fpc = fpc)
dclus1_yourexample <- apiclus1 %>%
as_survey_design(ids=dnum, weights = ~pw, fpc = ~fpc)
#> Error: Formula shorthand must be wrapped in `where()`.
#>
#> # Bad
#> data %>% select(~fpc)
#>
#> # Good
#> data %>% select(where(~fpc))
Created on 2021-11-23 by the reprex package (v2.0.1)