Multiple spotlight won't work with Livestream

there is! we can only spotlight a person on live stream

The livestream should show whatever is shown in the Zoom meeting.

Also please make sure u choose correct view if u are using webinar : 

Attendee View: Set the video layout that the attendees see during the webinar. By default, they see the same view as the host (the host's default view is gallery view).
Follow Host's View: Participants will see the same view that the host is using, whether active speaker view or gallery view. If the host is sharing their screen, the attendees will have side by side mode with the host's share and the active speaker's video. The attendees can adjust the share and video size.
Speaker: Speaker view switches between the active speakers in the webinar, with other video panelists above the active speaker when not speaking.
Gallery: Gallery view presents either 25 or 49 participants (if enabled in client Settings) on the screen in equal size. If there are more panelists than allowed to fit, multiple pages of gallery view will be created.

While on recording you can check here : https://support.zoom.us/hc/en-us/articles/360025561091?mobile_site=true

Hope it helps! please like and mark this as solution so whenever someone has the same question this content will help.