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What about search capabilities? the search power of gmail is awesome:

Fastmail supports basically all of that, plus some extra capabilities: https://www.fastmail.com/help/receive/search.html

If you depend on Google suite, you might miss out on features provided by the online office tooling.

They lack automatic translation of emails. Not a big deal, but in gmail it's one click away and with fastmail you have to copy-paste.