Never faced this before, so just spitballing…
What sort of events do people usually like? What has been popular in the past? If it’s, say, bowling, then that’s one thing… if it’s a “socially lubricated” (aka alcohol involved) event/party, that’s something different. If everyone supplied their own favourite libation, you could come up with some sort of a party game you could play on a webcam or online.
Also, depending on the group size(s) something as simple as Monopoly or Settlers of Catan could be played with a small group if someone in your group was willing to be a non-player (the banker) and operate the board while others called out actions to them. Just make sure you used rules to keep the game moving quickly (or ending quickly.)
With some pre-planning and pre-communication, you might be able to do some sort of murder mystery type game online.
The official Cards Against Humanity is probably too far away from work acceptable… but you might be able to come up with your own cards (and even involve the whole team in farming work appropriate content.) I think there are still free online games where you could play together while supplying your own cards (but I don’t know this for certain.)
If you can break people into smaller groups, you could break them off to solve a problem/puzzle as a timed challenge focused on team building. A really clever person (someone far more clever than me I’m sure) could come up with some sort of “virtual escape room” type challenge.
Whatever ideas you come up with, if you want competitive behaviour, and you have a budget, offer to have a special meal delivered to their home (aka uber eats or whatever) if they win.