How to specify an imputation model so that the resulting imputed variable approaches to a specific distribution, mean and standard deviation

Question

In a survey dataset I have a variable that has measurement error. I want to impute new values to it. I have a training dataset that includes surveys from past years that have common variables, so I want to use the correlations of the covariates in the imputation. Also, I know some things about the distribution of the target variable:

1. It is normal
2. The true mean
3. The true standard deviation

I have been suggested to use a bayesian regression to incorporate these priors as well as the covariates. In most forums, I have seen that this is done with stan/brms models. However, I know little about this kind of models.

Therefore, in short, I am looking for a code in R that is able to replace values with measurement error so that the resulting imputed variable has a normal distribution, the known mean, the known standard deviation and is in accordance with the covariates of the training dataset.

Here I include a replicable dataset on which the code I am asking could be applied:

# Set seed for reproducibility
# set.seed(42)

# Number of observations
n <- 1000

# Simulate 'variable_with_error' with random measurement error
measurement_error <- rnorm(n, mean = 0, sd = 1)
variable_with_error <- rnorm(n, mean = 0, sd = 1) + measurement_error

# Create some predictor variables
predictor1 <- rnorm(n, 0, 1)
predictor2 <- rnorm(n, 0, sd = 1)
predictor3 <- rnorm(n, 0, sd = 1)

# Combine into a data frame
df <- data.frame(
  variable_with_error = variable_with_error,
  predictor1 = predictor1,
  predictor2 = predictor2,
  predictor3 = predictor3
)