We have live streamed events. Our vendor would switch using multiple AJA SDI input dongles with Wirecast. They streamed to a CDN with the stream behind a pay wall on a private website. The issue with Livestream, Youtube, etc is they are designed to be public. If the client wants to control access then you need a somewhat custom solution.
You could of course also use a traditional switcher and send a single signal to your live streaming encoder, and also record to a ninja or whatever tech you prefer, but you still need a way to keep the content private.
We recently started using Zoom for a replacement for Webex. It seems pretty reliable and they have a webinar platform with some 3rd party pay wall options, but a lot of attendees can get expensive.
The other big issue can be getting adequate internet bandwidth and firewall access in the event venue, be it a hotel, conference center or corporate offices. That aspect can take the most time to plan, but being on a private website can help get buy-in.
Mike