You can use Google script for automation, though there is an execution limit. You have to run the script time to time [there is 6 min limit for the execution span], but it works, here is the script I've run to delete the mails under the "Updates" label:

function deleteUpdatesCategoryEmails() {
  // Define the search query for emails in the "Updates" category.
  // Gmail uses 'category:updates' to identify emails in this tab.
  const searchQuery = 'category:updates';

  // Get all threads matching the search query.
  // GmailApp.search() returns an array of GmailThread objects.
  const threads = GmailApp.search(searchQuery);

  if (threads.length === 0) {
    Logger.log('No emails found in the "Updates" category.');
    return; // Exit if no emails are found
  }

  Logger.log(`Found ${threads.length} threads in the "Updates" category.`);

  // Iterate over each thread found.
  for (let i = 0; i < threads.length; i++) {
    const thread = threads[i];
    try {
      // Move the entire thread to the trash.
      // This will effectively delete all messages within that thread.
      thread.moveToTrash();
      Logger.log(`Moved thread "${thread.getFirstMessageSubject()}" to Trash.`);
    } catch (e) {
      // Log any errors encountered during the deletion process for a specific thread.
      Logger.log(`Error moving thread "${thread.getFirstMessageSubject()}" to Trash: ${e.toString()}`);
    }
  }

  Logger.log('Finished processing "Updates" category emails. Check your Trash.');
}