How Do I Congratulate the Winner of My GIveaway?

There is no such an option to directly send message to people on this site. You don't need tho. Good thinking actually but even if you do somehow they won't care. It's enough to make giveaways if you ask me.

You could send them an Email.

I handle it in a way that when they thank me for the game, I congratulate them for winning it. (and if they don't thank me, they'll get a spot on my blacklist)

You could post in one of their old giveaways, or you wait until they say thank you and reply to it. (second option is way better imo)

Well, I add all my winners on Steam and try to have a conversation with them before sending the gift. (Even if it's for a key... and even though I suck at conversation-ing. XD)
(Then again, I also heavily restrict my giveaways in hopes the game would go to someone who would actually play it... not sure if adding them would work with public giveaways... :/ )

Whatever you do (and I can tell from the rest of your posts it's more about trying them to activate the GA ASAP than congratulating them), don't leave a comment on their Steam page talking about steamgifts.
That'll get you a community ban on Steam. Others have tried.

No need to send a message to congratulate the winner, Steamgifts already does it automatically by email.

After the winner has added the game to their Steam account, a polite one will usually thank you on the giveaway page. You can then reply to their message to congratulate them if you’d like.

Otherwise, especially in case of issues (such as a winner being slow to claim their prize), you can send them an email to try to get them to react. However, I don’t recommend using email just for a standard (congratulatory) message. You can find the winner's email address by clicking on "Winners" in the left column of the giveaway page.

Wait for them to say thank you and respond with a nice "you're welcome" type message is the only way to go.