RHEL 10 and clones are using an x86_64-v3 baseline, as are CachyOS, PikaOS and some other niche distributions. Between the limited package set of RHEL (partially mediated by EPEL), Fedora ELN not being recommended for production use, and the glibc-hwcaps proposal not getting momentum, is there any way to use this advanced instruction set?
In general v3 is only useful to a limited number of programs.
For the rest make no measurable difference.
Fedora is packaging thoses programs that can be improved with the v3 instructions along side a version built for all supported Fedora CPUs.
But this depends on the packager wishing to do the work to support the dual builds.
Do you have a specific program that you know improves with v3 instruction that you use?
Many programs work better in CachyOS than Fedora, including but not limited to many kirigami apps, Anki, cachy-browser (librewolf fork), pyqt apps like djpdf, etc. However, this may be due to either the x86_64-v3 baseline or the other optimizations they put in. Not being much familiar with the Arch or CachyOS composes and build systems limits my understanding on exactly which optimization plays a role here.
You don’t have to do anything to “use” x86_64-v3, other than run the latest stable Fedora release and keep your system up-to-date.
As for CatchyOS, it seems to be very much bespoke, and Fedora is very much vanilla. The Fedora community prefers getting better compiler flags into upstream projects, so all users on any distribution get a better experience.
Work put into Fedora also reverberates into enterprise RHEL. Changes made now in Fedora must, to an extent, take into account the long term goals of RHEL, which places additional guardrails on just how much developers can change and innovate in a given time frame.
They’d probably run better under Gentoo 
I’m not sure how to have Fedora use v3 system-wide, but generally speaking, if the distro maintainers haven’t done it yet on a fast-moving mainstream distro, they might have good reason for it.
What do you really want v3 for specifically?