Alvarez has been very good, but not head and shoulders above his teammates and opponents, just like Bellingham has been in La Liga & the two UCL games so far.
Statistically Bellingham has 13 G&A in 10 games, Alvarez has 11 G&A in 13 (Transfermarkt). Also Bellingham is better than pretty much every other area of the game (passing, duels etc) and according to WhoScored he averages a 8.26 rating in La Liga, while Alvarez is on a 7.32 in EPL. Bellingham has 6 MOTM awards, while Alvarez has only one, against Red Star in UCL.
So yeah, I think Bellingham has been better by any means.
Guti is a legend for us, but I don't understand this "throne" thing. I've seen other people saying things like "Bellingham is gonna dethrone Haaland and Mbappe". The current Ballon d'Or holder is still Benzema, the current FIFA The best award belongs to Messi. Vinicius, Mbappe and Haaland have never been the best players in the world yet and as for Bellingham, he's close, but it's too soon to say.
Even if Haaland wins the Ballon d'Or ahead of Messi, Mbappe will most likely barely finish in the top 5 and that's mainly because of his WC final performance and his overall popularity.