I always give my email. You can set up a free gmail account just for Upwork if that makes you more comfortable.
I frequently give out my phone number and arrange a time for a telephone interview because my understanding is that the platform video chat is hopeless.
Only you can decide if it's safe. I work exclusively for attorneys so it doesn't concern me as much.
The last time I called someone from my cell phone (because I hate skype), that lady had the nerve to call me at 9:30pm lol. She was local to me too so it wasn't even a time zone thing. That job went into dispute too. It was so fun knowing the contract is going south and trying to force her into leaving messages on Upwork.
I had another client from a long time ago text me at all hours too. It gets to be no longer a quick email (I don't charge for any of this) into being available at all hours, which at that point I want to get paid for it.
Brandon: Upwork has no rules governing what contact information you may provide to clients or potential clients. So ultimately you need to make your own decisions and your own rules.
The other posters in this thread already shared useful insights and experiences.
Feel free to use project-specific or "throwaway" email addresses and phone numbers. You never need to provide your "prime" personal contact info. Through Google Voice and other services you can obtain free phone numbers.
Some freelancers tell clients that they can contact them using Upwork Messages during the interview stage, and only provide phone number or email address after they are hired. Some freelancers share contact information. Some never do.