In the new version, I chopped a few trees to the right of the start position. When I approach the tree indicated it 'shimmers' and disappears then reappears roughly when I get to the first boulder
Probably you mean the "fading" between different LOD levels? I.e. the closer you get to the tree, the more detailed it will be. In the new version, trees are getting replaced with lower-detailed versions the further you go away from them. At some point, they're replaced with a 2D billboard, and if you travel even further, they will become fully invisible. This is basically done for performance reasons, but in most cases it shouldn't be that much noticeable.
However, this behaviour is controlled by the "LOD Bias" slider in the graphics settings in the "View Distance" section: The lower the value, the sooner the tree gets replaced by a 2D version (or culled completely). The default value is 100%, but if you set it to a very low value (< 40-50%), you will mostly just see 2D trees (unless you get very close to them), and small trees may get culled very quickly.
To improve this situation, you can set a higher value for "LOD Bias" (for instance, at 100% that shouldn't be a big issue anymore), but the higher the value, the bigger the impact on performance.
"LOD Cross-Fade" in the graphics settings is indeed responsible for the "shimmering" - it tries to achieve a smoother transition between different LODs - disabling this may even slightly improve the performance, but this will result in popping (i.e. abrupt switchovers between different LODs).
Incidentally, the performance seems much worse on my PC than many comparable 3D games - I have to turn off almost all visual effects but most especially grass which absolutely kills the framerate. I have an AMD Ryzen 5 2600, Radeon RX7 8gb, 16gb RAM running MX Linux. Not exactly cutting edge but even lowering the resolution, performance isn't good. Any help/suggestions welcome!
Your CPU and RAM are totally fine, but the bottleneck is the graphics adapter. It is an integrated RX Vega 7 graphics adapter? In this case, it doesn't meet the minium requirements of the game unfortunately 
The game requires a graphics card which is at least comparable to a NVIDIA GT 1030 (or the much older GTX 650 Ti) in terms of performance. Or more precisely, a graphics card which has a score of at least ~ 2500 on passmark (the Vega 7 isn't listed there unfortunately, but a Vega 6 has a score of 1000, while the Vega 8 has a score of 1500, so the Vega 7 probably has a score between 1000 and 1500).
Our low-end test rig has a GT 1030 (+ a 12 years old Phenom II X4 955 CPU and 8 GB RAM) and we achieve roughly 30-40 FPS on low/medium settings (shadows and grass enabled) on Linux Mint - but the GT 1030 is twice as fast as the integrated Radeon, which makes a big difference 
Unlike the Java version, the new version has an upfront cost - this enables the game to achieve much better framerates on larger view distances or complex scenes (i.e. consisting of very detailed buildings). In other words, you lose a lot less FPS compared to the Java version if the scene gets more complex. But the downside is that it runs terrible on low end graphics adapters...
Unfortunately it's also a bit difficult to compare it with other 3D games. Due to the randomly generated voxel terrain, there is a lot less room for optimizations from a technical point of view. A game with a static, pre-designed world, for example, could run a lot better (even if it has better graphics), simply because a lot more optimizations can be done in that case and less things need to be rendered in realtime. But even if you compare the game with another voxel game (like Minecraft), i.e. a game with a fully modifiable terrain, it still depends on various factors 
Do you have any plans to get a newer graphics card in the near future? That will certainly give you a major FPS boost. But other than that, I'm afraid there isn't much you could do to improve the framerate, except disabling most visual effects - when hovering various graphics settings, the game shows a tooltip indicating the estimated impact on performance (according to your screenshot, you could disable volumetric clouds and shadows - they still have a considerable impact on performance)...
However, it is our intention to add support for AMD FSR in the near future (for both DirectX and Vulkan), which will probably give you a small FPS boost. Probably it won't make a huge difference with that graphics adapter, but it could possibly improve the framerate by 10-30%.