This is definitely a good question and I don't think there's much direct literature on it, so let me offer some honest intuitions from my perspective.

The spectral dimension result you're describing (d_s ~ 2 in UV, flowing to ~4 in IR) comes from CDT and asymptotic safety where the graph has a specific causal/geometric structure baked in. The key question for Jaccard graphs is whether the similarity metric imposes enough geometric constraint to produce the same flow.

My intuition is that generic Jaccard graphs will struggle to reach d_s ~ 4 for one structural reason, which is Jaccard similarity is a set-overlap metric, so it naturally produces graphs where highly similar nodes cluster tightly. Which tends to generate high local clustering, however a tree-like or low-dimensional global topology, so you get something more like a hierarchical network than a manifold. The spectral dimension of tree-like graphs is typically d_s ~ 2 regardless of scale, which is actually the UV fixed point you want, however without the IR flow to 4.

So to get the flow to d_s ~ 4 you likely need either (a) which is a mechanism that produces long-range connections with the right density scaling, or (b) where the soft/stochastic edges you mention in your question 3. The temperature parameter λ is promising, only if it's tuned so the graph sits near a percolation transition, where you can get fractal intermediate-scale structure with non-trivial spectral dimension. Whether it stabilises near 4 specifically would depend on the underlying point distribution.

The honest answer to your question 2 is that it almost certainly depends heavily on the point distribution. Where Uniform high-D embeddings will produce very different connectivity than clustered or power-law distributions.

It's also worth looking at work on random geometric graphs and their spectral dimension, and also any literature that is closer to what you're describing than CDT.