Janzer's conjecture on blowups of spiders

Let $s\geq2$, $k,b,t\geq1$ be integers. Let $S$ be an $s$-legged spider whose longest leg has length $k$, and suppose that $e(S)=(s-1)k+b$, where $0\leq b\leq k$. Let $t*S$ denote the union of $t$ copies of $S$ sharing the designated roots as in the spider blowup construction. Janzer's conjecture.

$$\mathrm{ex}(n,t*S)=O\left(n^{1+\frac{s-1}{(s-1)k+b}}\right).$$

This conjecture concerns extremal numbers of blowups of spiders and is motivated by results for subdivisions of complete bipartite graphs and related graphs. The source presents it as an open conjecture.