For me probably the reason was that the channel was not a brand account - as As @LFS above mentioned in some comment (actually that channel was not converted to branded account yet, so I cannot tell for sure, I am just guessing that it was the reason; but I think it is a good guess, because when I use the same actions for Manager account on other channel accounts that are branded, then everything)
I was given Manager access to a YouTube channel (that channel was not a branded account but still the owner could invite me to be a Manager), but I did not have live streaming option (i.e. live button not available in YT Studio main page for that channel).
Also, when I crafted the URL manually (https://studio.youtube.com/channel/CHANNELID/livestreaming/manage) I couldn't do anything, but there was only a message "Only the channel owner can access live streaming".
It was true - the owner of the channel had a live streaming button on YT Studio, and could enter live streaming and do everything normally.