Timelines and universes, as terms, are interchangeable because each timeline is its own universe. Nexus events are events that drastically alter the predetermined path for those timelines or universes as according to Kang's Sacred Timeline and if allowed to go beyond a certain point those nexus events give birth to entirely new universes.
Combining what The Ancient One said in Endgame with what we learned from Loki, a simple example is... Taking the Time Gem from 2012 is a nexus event that creates a new timeline, a new universe, and the red line - the point of no return for that timeline or universe - is when Dormammu shows up in 2016 and Doctor Strange doesn't have the Time Gem to stop him.
I think there's where a lot of people are confused. Timelines and Universes are not interchangeable, they are two separate things. Timeline is the course of events that happens over time, in this case, the Sacred Timeline is a predetermined set of events created by HWR. Universe is just the universe as you know it.
HWR found a way to wrangle all the universes into one timeline. So up until episode 6, all the universes aka multiverses exist within HWR's Sacred Timeline and adhere to all the predetermined events set by HWR himself. Within this context, each timeline is NOT it's own universe because there is only one timeline (the Sacred Timeline) and all the universes exist within it.
When Sylvie killed HWR, the multiverses are not bound by the Sacred Timeline anymore. Now, universes could exists on their own timeline like you said. That means variants of HWR aka Kang, Ramatut, Nathaniel Richards now can exist. Any of these variants could potentially win the Multiversal War and create their own version of the TVA. It is also why Loki is sent back to a different TVA even when it exists outside of time.