Will the iPhone 6s become obsolete soon?

With it supporting iOS 15, you have a year at least on Apple's side for optimal support, you will probably have app support and security updates for another year even if iOS 15 is the last version supported. Officially, we probably aren't going to get more information until iOS 16 is announced if there will be any more support for the iPhone 6s. If you recently had the battery replaced and are still getting good service from it, there is no immediate reason to upgrade, but be ready to bail if you absolutely must have the latest iOS. You also have several more years of carrier support as well.

As far as the upgrade path, we are in a unique situation with a lot of options for a similar size device. You have the iPhone SE, iPhone 12 Mini, and of course iPhone 13 Mini. If you would like to upgrade to a larger handset, you may want to consider the iPhone 11, iPhone 12, or iPhone 13. My recommendation is to purchase, and if needed finance, through Apple. This gives you an unlocked phone which gives you the ability to switch carriers at any time, add an additional line on another carrier at any time, as well as use international SIMs. All models mentioned support dual SIM and dual standby, while the iPhone 13 supports dual eSIM and dual standby.

iPhone 6s is eligible for iOS 15. We don't know when Apple will stop supporting it, but it is the oldest iPhone eligible for the current iOS and it's now been getting support for 6 years, which is longer than any iPhone in the past. So it stands to reason, it's end of support is not too far away, but the date is unknown to anyone on this forum as this is a user to user only forum, and Apple isn't here.

There have been 8 different models of iPhone since the iPhone 6s, any of them can replace it. You can go and buy any iPhone you want to replace it.

But as mentioned it is still supported and will be at least for the next year fully and probably a couple more years after that for security updates if iOS 12.5..5 is anything to go by.