They're not an old team or past their peak. New manager for sure but he's come in to a better squad than people think and already has them playing well.
Allison is 31, Trent is 25, VVD 33 (getting on), Konate 25, Robertson 30, McAllister 25, Szobozlai 23, Gravenberch 22, Salah 32, Diaz 27 and Jota 27. Only Salah and VVD are getting on but players don't suddenly need to be thrown in the dustbin anymore at those ages. Not to mention their backups are guys like Gakpo, Nunez, Chiesa, Elliot, Bradley, Gomez, Endo, Tsimikas etc.. they have 4 30+ players in a squad of 25 and ones a goalkeeper and one a CB. The other is still the best winger in the league if not what he once was.
This Liverpool team are closer to coming in to their peak than passing it. Last season was their transition season and they've started this season playing better football than either City or Arsenal despite the Forest blip. They have had a relatively easy start by comparison, particularly compared to you guys (who have had it rough) but they lead the league in xg, xg against and expected points so far and just twatted AC Milan at the San Siro. All metrics suggest they'll be a tougher nut to crack this season.
While I'm always slow to trust givemesport they suggest Liverpool have a younger squad than both City and Arsenal. 25.9 vs Cities 27 and you guys 26.5 and all 3 are in or around the sweet spot where league winners usually sit. And the numbers look about right.
https://www.givemesport.com/average-age-every-premier-league-squad/
Transfermarkt have you guys as the youngest at 25.5 and Liverpool at 26.5 but again my general point is that that all squads are sitting at a pretty good age relatively.
https://www.transfermarkt.co.uk/premier-league/altersschnitt/wettbewerb/GB1
People look at this Liverpool team as some dads army because of VVD and Salah but they're far from it. Its pretty much a new team Klopp started building a couple of seasons ago. And they have of course regardless of how much it pains me to say it, a mentality that runs right though the club, like when Benitez won a CL with the worst team ever to play a final. Give them momentum and they'll absolutely pounce on it.