The first leg of the Champions League win against PSG means a lot to Liverpool and therefore they might be more comfortable facing Southampton. But I don't agree if the match against Southampton is considered easy, of course because Liverpool must do their best not to lose points in the next match. Southampton is certainly not favored, but they also have a chance to win points as long as they are able to take advantage of the opportunities available.
The good news is, Liverpool are playing at home in their next match. Liverpool are favourites to win 3 points at home againt Southampton, but they must still maintain their focus even though losing 1 match will not really put them in danger.
I have the same thought as you and I have an assumption that Liverpool even though they are playing at home, will definitely not use some of their main players to maintain the players' physical condition. However, if they still use the main players, I am sure their performance will not be too optimal which can endanger the players' physical condition. While there is still a second leg match in the UCL. So, if Southampton knows this, they will definitely try their best to use tactics that can get a draw. A draw can happen to share points as you said.