Per NMDOT's Roadway Functional Class online map, NM 461 (Coyote Station Lane) is no longer in the state highway system. The cattle grates visible in GMSV don't mean it's a private road (probably just it's in open-range country, where cattle needs to be kept off major roads but not the minor ones), but it's still not a state highway.
NM 355 still is in the system, as of when the online map was updated in 2019. But it still gets deep-sixed from TM, as unsigned.
To go into my queue for removal and edits to the connecting US highways, with my next pull request as I wrap up some cleanup work in northern Nevada.
Update: Both routes removed from the HB in tonight's site update.