iPhone 6s to ios 15.1?

It was time to upgrade several years ago...

You're likely to have some apps that will not be compatible with iOS 15 at all.

Make sure you have any data stored inside of 3rd party apps stored somewhere else as well.

Password managers, so-called secure photo vaults, etc. have proven a problem after having been abandoned by the developers.

Sorry, but there is always a potential for issues when upgrading, regardless if it is over one major firmware version, or many. So there is no way to guarantee your iPhone will not be experiencing any of them. One critical area would be apps. The other is your data. You don't mention what your iPhone is currently running. However, if it's been awhile, you may have apps that won't run on the latest iOS version. For the latter, just be sure to make backups to either iCloud or a computer.

The update is compatible with your iPhone 6s, I loaded on my work issued 6s with zero problems. The only problem you might encounter is the speed of processing from the relatively slow processor (compared with later models) while the update installs, so leave yourself an hour or so when you can be without the phone.

Yep, it's been awhile since you last upgraded this phone. Regardless, as long as it is working for you, there is no pressing need to upgrade ... except potentially for security reasons. The key is that you will not be easily be able to do incremental upgrades ... so, it's pretty much iOS 15.1 or nothing.

As Brant_uk has mentioned, your iPhone is compatible with the (currently) latest iOS version. If nothing else, be sure to perform a backup, and give it a try. Worst case, you will find that you will want to upgrade to a newer iPhone anyways. ;)