Do you know the software to host a webinar?

#question

Hi everyone!

Because of COVID-19 my client's trainers are restricted to go to business trips but have to land the same count of workshops annually.

So we decided to use a platform for webinars to do those workshops remotely but we can't find a solution.

We checked out YouTube Live and some SAAS solutions but they don't meet the client's requirements.

What we need:

Ability to integrate all functionality (video stream, chat room, etc.) to our website;
Ability to record webinars and host those videos on our website in the archive;
Ability to style UI of the player and chat (branding);
The solution can be paid or some OSS projects as well;
The client doesn't want to show any attribution (I, personally, think that it's okay and even great to show solution attribution).