My 2023 predictions, as with last year based on my instinct:
Red Bull and Verstappen will continue to be the team and driver to beat, but they won't win as many races as I expect Mercedes to be more competitive than last year (not to mention more competent than Ferrari last year). Perez will win one race (at one of the street circuits) but won't finish in the top four of the championship
At Ferrari, Charles Leclerc will continue to largely outpace Carlos Sainz and further add to his impressive tally of pole positions, although he will again qualify on pole more often than he wins. Leclerc will again narrowly take second place in the WDC (see below).
Hamilton and Russell will be relatively evenly matched over the season. Mercedes will a lot more competitive from the beginning of the year though so both drivers will win multiple races and finish above Perez in the championship. They will take second place in the constructors ahead of Ferrari, but Leclerc will finish ahead as he will regularly beat Sainz whereas the Mercedes drivers will take points off each other.
At Alpine, Esteban Ocon will continue to deliver respectable if not outstanding performances, putting him ahead in the battle of the two French drivers.
Lando Norris will continue to impress for McLaren and will score enough points to ensure fourth place in the WCC as he outperforms both Alpine drivers. Piastri's level of performance will be comparable to Ricciardo in 2021 (albeit not a race winner as McLaren will not be competitive enough), I predict he will finish around 11th in the WDC.
Alfa Romeo Sauber will be mostly anonymous, more like their 2019-21 performances than the first half of last year. Zhou will be closer to Bottas in points this year but the team will finish near the bottom of the standings.
Aston Martin should improve with Fernando Alonso (more motivated than Vettel) comfortably beating Stroll. Alonso will finish in the top 10 of the championship but Stroll won't score enough points for the team to finish higher than sixth.
Haas won't be quite as quick as last year, but Hulkenberg will get better results than Mick Schumacher and therefore the team will finish in a similar position. Magnussen will be the stronger of the two drivers however.
At Alpha Tauri, Nyck De Vries will emerge as the stronger of the two drivers and Yuki Tsunoda will be replaced after next season, quite possibly with Liam Lawson coming in.
Williams will continue to struggle and finish last in the standings but both drivers will score points, Alex Albon will continue to impress and will be linked with a move to one of the stronger teams.
I don't predict a radical change in the competitive order for next season, as I expect the top three teams to continue to dominate the podium and if any other driver manages to win it will be in unusual circumstances (think Italy 2020 or Hungary 2021). Of the other seven teams, I predict Aston Martin will be the most improved team compared to the beginning of last season while Alfa Romeo Sauber will have lost the most ground.