Twitter provides access to your old tweets and performance metrics, but it’s not the same for other Twitter profiles. You cannot download old tweets of other users directly from Twitter’s official website.
You will have to use Twitter API to gain access to this data. Although, downloading old tweets using the Twitter API requires coding experience. If you don’t have the required expertise or the resources to overcome that, you should use a third-party analytics tool such as FollowersAnalysis (https://www.followersanalysis.com/blog/download-old-tweets/). It allows you to download old tweets related to any hashtags, keywords, @mention, or even tweets posted by a specific account.
If you have academic access (https://developer.twitter.com/en/products/twitter-api/academic-research) there are many tools you can use for that, one of the tools I use is the academictwitteR package in R: https://github.com/cjbarrie/academictwitteR
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