Also, we usually do directly below:
mu = alpha + beta_1*x['feature_1_2'].values
Target = pm.Normal('target', mu = mu, sd = sigma, observed = model_output)
As the uncertainty in mu is a bit useless, it just being push to the sigma, which means your model currently is equivalent to:
mu = alpha + beta_1*x['feature_1_2'].values
Target = pm.Normal('target', mu = mu, sd = tt.sqrt(sigma**2+1**2), observed = model_output)