Search Bar Not Working

A first practical advice. When you paste code here, use "Paste and match style" to avoid all the extra blank lines that make code hard to read:

Code Block 
func tableView(_ tableView: UITableView, numberOfRowsInSection section: Int) -> Int { // determines what data source should be used when user types
        if isFiltering {
            return filteredArticles?.count ?? 0
       }
        return articles?.count ?? 0
    }
    
func tableView(_ tableView: UITableView, cellForRowAt indexPath: IndexPath) -> UITableViewCell {
        let cell = tableView.dequeueReusableCell(withIdentifier: "cell1", for: indexPath) as! NewsTableViewCell
        let news: Articles
        filteredArticles = articles
        if isFiltering {
            news = filteredArticles![indexPath.row]
        }
        else {
            news = articles![indexPath.row]
        }
        cell.authorName.text = filteredArticles?[indexPath.row].author
        cell.headLine.text = filteredArticles?[indexPath.row].title
        cell.newsImage.downloadImage(from:(self.filteredArticles?[indexPath.item].urlImage ?? "nill"))
        cell.timePublication.text = filteredArticles?[indexPath.row].publishedAt
        if let dateString = filteredArticles?[indexPath.row].publishedAt,
        let date = indDateFormatter.date(from: dateString){
                   let formattedString = outDateFormtter.string(from: date)
                   cell.timePublication.text = formattedString
               } else {
                   cell.timePublication.text = "----------"
               }
        
               return cell
           }
   
    func updateSearchResults(for searchController: UISearchController) {
        let searchBar = searchController.searchBar
        filterContentForSearchText(searchBar.text!, articles!)
    }
    func filterContentForSearchText(_ searchText:String ,_ category: [Articles]){
        filteredArticles =  articles?.filter({ (article:Articles) -> Bool in
            return article.description.lowercased().contains(searchText.lowercased())
            
        })
        table_view.reloadData()
    }

Now, back to your code.

In comment line 1, you say:

func tableView(_ tableView: UITableView, numberOfRowsInSection…) determines what data source should be used when user types

That's not the case, I hope you don't count on this for the selection.
But effectively, isFiltering is doing so.

I don't understand the logic.
Line 11 (my numbering), you set filteredArticles to articles.
What is the insterest then of this filteredArticles ?

Shouldn't the function be like :

Code Block 
func tableView(_ tableView: UITableView, cellForRowAt indexPath: IndexPath) -> UITableViewCell {
        let cell = tableView.dequeueReusableCell(withIdentifier: "cell1", for: indexPath) as! NewsTableViewCell
        let news: Articles
	        var articlesToUse = articles	// by default
        // Get rid of this   filteredArticles = articles
        if isFiltering {
			    articlesToUse = filteredArticles
            // news = filteredArticles![indexPath.row]
        } /* Remove
        else {
            news = articles![indexPath.row]
        } */
	     news = articlesToUse![indexPath.row]
        cell.authorName.text = articlesToUse?[indexPath.row].author		// instead of filteredArticles
		// The same on following lines

Question: why do you make articles an optional ?

Note: use of underscore as in table_view in discouraged in Swift.
You'd better give a meaningful name with CamelCase writing, for instance:
articlesTableView

There are some other errors probably:

news is never used. Why do you declare it ?

You use row somewhere and item in other place ?

The error is in fact on line 40:

Code Block 
            return article.description.lowercased().contains(searchText.lowercased())

you should not filter on description, but on content.

if you change with

Code Block 
 return article.title!.lowercased().contains(searchText.lowercased())

Then you get the correct selection.

Note : there is a remaining error: image is not corrsponding to selected article

You have to replace line 20 (of my counting)

Code Block 
        cell.newsImage.downloadImage(from:(self.filteredArticles?[indexPath.item].urlImage ?? "nill"))

by

Code Block 
        cell.newsImage.downloadImage(from:(articlesToUse?[indexPath.row].urlImage ?? "nill"))

Now it works perfectly correct.

The full cellForRowAt func code is:

Code Block 
    func tableView(_ tableView: UITableView, cellForRowAt indexPath: IndexPath) -> UITableViewCell {
        
        let cell = tableView.dequeueReusableCell(withIdentifier: "cell1", for: indexPath) as! NewsTableViewCell
        let news: Articles
        var articlesToUse = articles    // by default
        if isFiltering {
            articlesToUse = filteredArticles
        } 
        news = articlesToUse![indexPath.row]
        
        cell.authorName.text = news.author
        cell.headLine.text = news.title
        cell.newsImage.downloadImage(from:(articlesToUse?[indexPath.row].urlImage ?? "nill"))
        cell.timePublication.text = news.publishedAt
        
        if let dateString = articles?[indexPath.row].publishedAt,
            let date = indDateFormatter.date(from: dateString){
            let formattedString = outDateFormtter.string(from: date)
            cell.timePublication.text = formattedString
        } else {
            cell.timePublication.text = "----------"
        }
        
        return cell
    }

@Claude31 Thank you for the help. Ive been able to spot the bugs. Can you please recommend a tutorial that provides a comprehensive description on how to debug ?

Great if it works now.
Here is a tutorial that may help: https ://www.hackingwithswift .com/read/18/overview

Debug is a question of method.
I can explain how I did with your code.

1. Just read the code carefully. And notice the warnings as "news is never used" You will find a lot of issues.

2. When the table didn't show anything, I added print statements in several places to monitor the count of articles and filteredArticles. I noticed that filteredArticles was always empty.

3. Then, the hard part: you need to find out why ? It was likely that filteredArticles did not find any. So, needed to look at:

Code Block 
    func filterContentForSearchText(_ searchText:String ,_ category: [Articles]){
        filteredArticles =  articles?.filter({ (article:Articles) -> Bool in
            return article.description.lowercased().contains(searchText.lowercased())
            
        })
        table_view.reloadData()
    }

4. For testing, I added a print(article.description) and got 50 lines as:
<covid_news.articles: 0x600003f67e40>
So, it was clear that was the the content we wanted to look at.

5. Thus, I looked at the Articles and decided to replace description by author!.
I tested and saw it worked when I typed Kim for instance.
Looking further, I found that the content was in title, so I replaced description by title!.
And it worked smoothly.

6. Testing further showed that images were no more matching articles after filter. That was because I did not use the right array in:
cell.newsImage.downloadImage(from:(articlesToUse?[indexPath.row].urlImage ?? "nill"))

So, as conclusion, debug is often a zooming in exercise. Guess and find where the problem could come from (which area), add a lot of print statement to localize precisely and then find the error and correct.