Heyo when open beta is available and if you are able to do so at that time, make sure to give it a good play for your system, that way you will have a much better idea.
I am in the same boat as you, I have an old xbox one s, I will be giving the open beta a good go at trying out the game for my system, I'm a little skeptical of it running smooth, but who knows maybe I will be and you will be surprised (hopefully)
Otherwise, about the new Xbox series S to the other person asking for an opinion on it for this game, if you are not worried about 4k resolution gaming at 120hz, whether you don't care , don't have the means to do so cause you would also need a tv and or monitor that supports that as well, I would say personally if you are most likely to put hundreds of hours into the game over time, like it will be your main game you primarily play ( that's what it is like for me or that is the plan anyway ) and are not in a hurry or just cannot get a ps5 or series X, I would say go for it, I mean I'm considering possibly doing the same thing and you'd save yourself some money, but I don't buy many games and not really interested in very many a very select few and BF2042 will be "my main go to game" unless I end up not liking it lol, but that's the idea for me. I don't care about 4k 120 and I am not willing to put out the money for a tv or monitor on top of that and paying scalper prices for the top tier systems.
Do some research on specs to make sure for yourself, I don't think it is a bad idea, it would for sure be a much smoother experience on the series s than say my old xbox one s, I might just do that myself, but like I said BF2042 would be the game that I would "shoot" for playing for a long time and sink a lot of free time into, also from what I have seen you would have a very much higher chance of securing a series S from a retailer, I suggest checking out Best Buy or Targets.
hopefully I maybe said something useful in here as an opinion on getting a series S for BF2042 I can blab blab a lot.
take care.