I have just started my free trial. I am creating new issues, but only New Feature and Task appear in the Issue Type drop-down. I reviewed the types in admin settings, and all looks fine (but then again, I'm new).
It's controlled by two things
1. Look at the "issue type scheme" for that project - I suspect you'll find it only contains those two issue types
2. Be wary of sub-task types - even though they are named in the issue type scheme, they will not appear on the drop-down because you can only create them from their intended parent
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