In addition to above advice,
See https://github.com/godotengine/godot/issues/45047
The best solution to this is to use edge padding, i.e. add at least a pixel border around each tile in your atlas - the problem is with the artwork. A lot of engines suffer with this problem. The legacy renderer used a hack in the shader to try and get around this problem, which you can try if you turn off batching, but performance will drop.
There is also a setting rendering/batching/precision/uv_contract
which you can switch on which may help with this.
I'm hopeful someone will put in support to make automatic bordered atlases (this is really Groud's area), but there has been no joy so far. I may if I get a moment try and put in a very basic version of this, but I'm not really familiar with the tile editor code.
An alternative which I may get around to is adding this extra border information to a new FVF for the batching and using a similar hack to the legacy renderer, but this isn't a great solution because it can cause problems on some hardware (I suspect the problems that required the nvidia_workaround are related to this) and it may drop performance, in some cases severely.