Office work? Yes. Gaming? eh..... Perhaps some older games, or newer games at ungodly low resolutions. If gaming is important to you, you really want a dedicated gpu.
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It's enough for LoL, CS, Dota2 etc
Better pick a Ryzen Laptop...
Office work can generally be done on any of the newer hardware so an i5 or i7 would work fantastic for all of that, but if you want to game you will definitely want something with a graphics card in it. Given that you are upgrading from (at this point) a fairly old laptop something with a rtx 4060 or even a 4050 would be worlds better for gaming. For a cpu you could easily downgrade to an i5 and that would be plenty.
So overall I would recommend trying to find something in a similar price class that has an i5 and a rtx 3060, 4050 or 4060. These graphics cards would all play games like the ones you mentioned (skyrim, fallout, and other older titles) at 1080p.
Google says i7-12700H has Intel Iris Xe Graphics G7 96EU GPU.
https://www.youtube.com/watch?v=6dNaqDwxW60
https://www.youtube.com/watch?v=oWeeM7YaSC0
You can see some tests of this GPU here. Looks like games like LoL, Dota 2, Valorant, Warframe, CS GO, GTA 5 work fine, but most AAA game will struggle to even reach 30 FPS.