Here’s my take on this situation.
Recovering deleted tweets can be tricky, as it often depends on timing. Your best bet is the Twitter Archive feature you mentioned. The major consideration here is when you last requested your data. The archive is a snapshot; if you requested it before the deletion, the tweets will be in that file. If you request it now, they unfortunately won’t be included. It’s always a good practice to periodically download this data as a personal backup for this very reason.
As for third-party tools, their effectiveness varies. They generally rely on accessing caches or public archives like the Wayback Machine. This can sometimes work for tweets that had high visibility and were indexed by search engines, but it’s not a reliable method for most content. It’s a trade-off between the definitive record of a pre-existing archive versus the long-shot chance of external caching.