What are the differences between kernel 5.15 and 6.1. What would be reasons to move to 6.1 now ?
It's the newest LTS, and OpenWrt releases are built on that type of kernels. At some point support for 5.15 will be dropped upstream which will make it unmaintainable for OpenWrt as well, so there is no incentive to stick with a certain kernel for eternity.
As for the differences between kernel versions, there's sites like Kernel Newbies that helpfully highlight changes between versions.
In addition to what @Borromini said, OpenWrt has traditionally moved the main branch to the most recent LTS kernel following a release. So after kernel 5.4 in 21.x, main went to kernel 5.10 for release 22.03, then main went to 5.15 which will be used for 23.05, now since 23.05 has been branched, main is being moved to 6.1 for 24.x and so on...
Not sure if this page describes changes from 5.15 to 6.1 or rather from 6.0 to 6.1, but you can see it's a lot
…and there are new developments just waiting for kernel v6.1. ipq807x already needs many backports from v6.1, the same goes for filogic 830 and ipq60xx will require v6.1 as well. The same goes for individual (addon-) device support, be it modern intel/ realtek ethernet cards, USB attached devices, etc or new features (e.g. MGLRU)
If you want to know the details, you'll have to wade through them, one by one. Other than that, the story is always the same, everyone actually doing development work is desperately waiting for the new kernel, as it provides new device support, an opportunity to drop all the backports needed previously, to have a development at least roughly capable to validate upstream development (and being able to submit tested patches) and to stay on top of upstream-maintained (LTS-) kernel versions.
Either you go with the times - or you go, with the times.
The search function of this forum will hand you the very same question (and answers) for v5.15, v5.10, v5.4, v4.19, v4.9, v4.4, …
It's only about v6.0 to v6.1, so you'll have to add the equivalent posts for v5.16, v5.17, v5.18, v5.19 and v6.0 as well.