Opt into the Steam Client Beta (in order to be able to actually run SteamVR v2); additionally, opt into the ‘beta’ channel for SteamVR. Be conservative with installing SteamVR updates sometimes, because it feels like Valve (or whatever contractor they hire) likes to break things randomly. Nonetheless, the beta channel has become fairly stable and reliable, weirdly more than the non-beta channel. There’s actually a lot more working now than there was a year ago (such as ‘desktop view’ and such in the SteamVR HUD, which would normally be finnicky, or not run at all).
Source: I use a Valve Index exclusively only on Linux on a near-weekly basis.