I also thought the match would be at least a draw but Liverpool couldn't come back with a win despite being even though they were ahead twice. I will especially blame Salah for this, he missed an easy goal and his performance has been a bit down lately. They may not have taken the match seriously after winning the league. Although the match against Brighton is not that important for Liverpool, I think they should have won with them. You are right that losing one or two matches may not hurt them but losing to a weaker team considering their own team's strength can be mentally damaging.
Even though the loss of Liverpool and win of Brighton would not have a significant effect on the table, it shows how competitive the teams are in premier league. It would be difficult for Liverpool to make a new record on stats as they won't be able to come near their own 2019-20 records.
As of Manchester City reaching champions league, I see they have more chances to qualify than Aston Villa, Chelsea or Newcastle. Chelsea would be in the largest trouble as they are facing Nottingham Forest which is keen on taking points. Newcastle and Aston Villa too have just a single match left while Manchester City has 2. Even though Chelsea, Newcastle and Aston Villa wins their respective matches, If Manchester city wins one and draws another, they would rise to the 3rd position. So its more like a battle between Chelsea, Newcastle and Aston Villa.