Is it okay to update an announcement topic that is over 60 days old? Do I need to start a new topic about my project?

I would also recommend starting a new one in most cases.

It's actually permissible to do either, but would be rude (and may get you a friendly warning from one of our moderators) if you did both, as we like everyone to have an equal opportunity to attract attention. In some cases -- usually involving a long-standing log of regular updates on the same topic -- people do prefer to maintain an older topic, but for most purposes you'll probably be better served by starting a new topic.

You can save yourself some effort by cutting and pasting some of the content if it helps you, and you might also consider linking to the original topic for context if relevant.