My understandings on the Fediverse is unclear right now. Will you be able to search for posts just as in stack overflow and reddit right now?
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You should be able to eventually, although it might take a little bit of time for search engines to catch up and start indexing the relevant pages.
It’s going to take some time for search engine crawlers to start indexing everything, but yes it will defintely be searchable in the future.
This has been discussed before in a few places. https://fedi-search.com/ seem like the site you are looking for. Full credit to Benjamin Pryor