Accessing and storing p-values from GARCH Model Fit output to assess the fit of my estimated models

Question

I have this loop.

with_progress({

    # Initialize the progress bar
    pb <- progressor(along = unique(pct_women_exec$ticker))

    # Precompute unique tickers
    unique_tickers <- unique(pct_women_exec$ticker)

    # Use lapply to fit models for each ticker
    fitted_models <- lapply(unique_tickers, function(ticker) {

        # Subset the data and external regressors for the current ticker
        y <- pct_women_exec[pct_women_exec$ticker == ticker, "ret.RF"]
        X1 <- data.frame(Mkt.RF = pct_women_exec[pct_women_exec$ticker == ticker, "Mkt.RF"])
        X2 <- data.frame(event_dummy = pct_women_exec[pct_women_exec$ticker == ticker, "event_dummy"])
        X2 <- as.matrix(X2)
        X <- cbind(as.matrix(X1), X2)
     
        # Define the specifications
        spec <- ugarchspec(variance.model = list(model = "sGARCH", external.regressors=X2), mean.model = list(armaOrder= c(0, 0), include.mean = TRUE, external.regressors=X))
    
        # Fitting the model                      
        fit <- ugarchfit(data=y, spec=spec)
        
        # Extract the standard deviation of sigma
        sigma_sd <- sd(sigma(fit))

        # Update the progress bar
        pb()

        # Return the fitted model and the standard deviation of sigma
        return(fit)

    })  
})

How can I access, extract and store the p-values for all of my estimated models for the diagnostics tests posted in the picture? I need it to assess the fit of my estimated models.

I tried all kinds of code but in particular I am given the error saying that I cannot access an S4 object using $.