After updating certain plugins, they may consume resources. Try deactivating recently updated plugins one by one to see if the speed improves. Enable caching plugins like WP Super Cache and check if images support WebP. If the theme is too heavy, it could also slow things down. If all else fails, consider switching to a faster server.

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Categorized pages and tagged pages to add noindex, in fact, depends on the structure of your site and the quality of the content. If just a pile of articles list, there is no substantive content, then add noindex on the good, there is no need to waste the search engine crawling budget. If the classification page has a theme to guide, conducive to content aggregation, then retain index, it can help you stabilize the internal chain structure. Tags page is usually too high repetition rate, the value of inclusion is not great. The general principle is - let the search engine to see the content in your favor, the rest will be shielded.