Interpreting the fit results when a spline term is used

I fit a model with brms in the following way:

e <- rnorm(100, 0, 0.1)
v <- rnorm(100, 0, 1)
data <- tibble(x=v, y=v+e)
form <- y ~ s(x)
fit <- brm(form, data=data, family=gaussian(), control = list(max_treedepth = 15, adapt_delta=0.999), iter = 9000, warmup=1000, cores = 4)

Then summary of the fit includes smooth term sds(sx_1) and population-level effects Intercept and sx_1. I have understood that the smooth term describes the wigglines of the spline, and the other terms describe the perfectly smooth term (linear component?). So, if sds(sx_1) is close to zero, then the spline is actually a line defined by the Intercept and sx_1 as the slope. But this does not seem to be the case as the value of sx_1 is 5.88, where 1 was expected. How should the coefficients be interpreted? And is it possible to decide based on the fit, whether the spline term should be included or be replaced by a linear term?

See here and the linked article by Tristan Mahr in the solution.