Residual using absolute loss linear regression For ordinary least square linear regression, we have sum of residuals as zero, what about the sum of residuals for  linear regression calculated using absolute loss?

Not really an answer, but I would say "not much" - see my above comment. Also invoking the following code a few times suggests we also cannot sign the sum of the residuals.
As you correctly point out, OLS is the technique that exploits orthogonality of residuals and regressors, which, if we have a constant, yields a sum of residuals of zero. As that is not the case for other techniques, there also is (at least to me) no reason to expect any special properties here.
library(quantreg)
set.seed(2022)
n <- 50
X <- sort(runif(n))
beta1 <- 2
y <- X*beta1 + rnorm(n,sd=0.5)
olsreg <- lm(y~X) # OLS linear regression
ladreg <- rq(y~X) # quantile regression
sum(resid(olsreg)) # basically zero
sum(resid(ladreg)) # not close to zero

