`/new` after `/model <custom-provider>:<model>` silently reverted to a
native provider whose static catalog happened to contain the same model
name (e.g. `deepseek-v4-pro` → native `deepseek` → 401).
Root cause at the `/model` writeback site: `HERMES_INFERENCE_PROVIDER`
was set unconditionally but `HERMES_TUI_PROVIDER` was only mirrored when
it was already set. On sessions launched without `--provider`,
`HERMES_TUI_PROVIDER` stayed unset, so `_resolve_startup_runtime()` on
`/new` skipped the explicit-provider early return and fell through to
`detect_static_provider_for_model()`.
Fix: set `HERMES_TUI_PROVIDER` unconditionally alongside
`HERMES_INFERENCE_PROVIDER` when `/model` lands. Keeps #15755's
invariant intact — `HERMES_TUI_PROVIDER` remains the canonical
"explicit this process" carrier, `HERMES_INFERENCE_PROVIDER` remains
ambient and does not short-circuit startup resolution.
Bug report and diagnosis: @Bartok9 in #16857 / #16873.
Fixes#16857