Mutate condition multiple columns loop dplyr

Question

I am trying to conditionnally replace values in one column based on the value from another column. The condition is simple, if a column's value equals "NAv" then I want to check the value in the neighboring column (left and then right) and if that neighboring column's value is different from "NAp" and "NAv" I want to report in the initial column either "ValueY" or "ValueX".

The tricky part is that I want to do it for multiple datasets (inside a loop) and the dataset don't always have the same number of columns.

However, the columns are named in a way that is easy to iterate over t1, t2, t3, etc.

Below is a reproducible example. Any help?

Fran <- data.frame (v1 = c("Fran", "Fran", "Fran"),
                  t1 = c("YES","NAv","NAv"),
                  t2 = c("NAp","YES","NAv"),
                  t3 = c("NAp","NAv","YES"),
                  t4 = c("NAp","NAv","YES")
)

Belg <- data.frame (v1 = c("Belg", "Belg", "Belg"),
                    t1 = c("YES","NAv","NAv"),
                    t2 = c("NAv","YES","NAv"),
                    t3 = c("NAp","NAv","YES")
)


ctr <- c("Belg", "Fran")


for (c in ctr) {
  for (i in 1:4) {
    t <- paste0("t", i)
    
    h <- (i-1)
    th <- paste0("t", h)
    
    j <- (i+1)
    tj <- paste0("t", j)
    
    a <- get(c) %>%
      mutate(across(starts_with(!!t), as.character)) %>%
      mutate(!!th = ifelse(!!th == "NAv" & !!t != "NAv|NAp", "ValueY", !!th)) %>%
      mutate(!!tj = ifelse(!!tj == "NAv" & !!t != "NAv|NAp", "ValueX", !!tj)) 
    assign(c, a)
  }
}