That is not a gaming laptop even if it is formally classified as one (although I'm not seeing that it is). It misses the mark in a few important ways. The processor is a U-series, ultra low power designed to conserve energy, not to run demanding programs like games continuously. Its graphics card is dedicated but not strong enough to carry more than the TS3 base game and maybe, if lucky, a couple of the early EPs. It does have a Solid State Drive (SSD) which is nice, but at 256 GB that won't be large enough as time goes by if you intend to store saved games and content on it and use it for other purposes as well.
I'm afraid you are going to have up the ante a bit if you can. Laptops that can carry the entire game start at $900 (USD). This one is on sale for $800 and hits all the right notes. MSI makes great (and expensive!) laptops, this one is on the lower end of its range and would be fine for TS3, probably TS4 as well. It doesn't have an SSD, but its standard drive is 1 TB so the fighting for drive space issue wouldn't be there unless you have a very extensive collection of high def videos and photos you intend to carry around.
https://www.amazon.com/MSI-GV62-8RD-200-Performance-Steelseries/dp/B07D4ZML7M