rustc hangs when compiling `varisat` (`-Znext-solver`)

Not sure if I should file a separate issue or not. Here is the minimized reproducer we saw in rust-lang/cargo's CI failure with the crate varisat:

/tmp/repro.rs

---cargo
[package]
edition = "2024"

[dependencies]
varisat = "=0.2.2"
---

fn main() {
    let _solver = varisat::Solver::new();
}

And run it

# this got stuck
cargo +nightly-2026-08-22 -Zscript check --manifest-path /tmp/repro.rs

# this succeeded
env RUSTFLAGS="-Znext-solver=coherence" cargo +nightly-2026-08-22 -Zscript check --manifest-path /tmp/repro.rs

# this succeeded
cargo +nightly-2026-08-21 -Zscript check --manifest-path /tmp/repro.rs

# this got stuck
env RUSTFLAGS="-Znext-solver=globally" cargo +nightly-2026-08-21 -Zscript check --manifest-path /tmp/repro.rs

Originally posted by @weihanglo in #160895

Start with the /tmp/repro.rs reproducer and run the listed cargo commands using the two nightly versions and next-solver settings. Compare the hanging and successful cases; done means the varisat check no longer hangs under the affected configuration, with the regression or relevant compiler area identified.