And the kids never use the master bath, right?
I’ve seen things get stuck inside toilets that successfully evade snaking - toothbrushes are in the Plumbers’ Hall of Fame for this. You can snake right past a toothbrush and not know it’s in there, but the next chunk of stuff will get stuck. Similarly, pencils, pens, popsicle sticks, mascara bottles, and similar long skinny things can do this.
Most often, the only cure is to take the toilet off and push the offending thing out from below. Yeah, I know. Ick.
Ten to fifteen year old low-flow toilets are junk, compared to what’s available now. If this was my house, I’d start by just replacing the toilet. I’ve had very good results with Toto. Eljer and American Standard also make “performance” toilets that are well-regarded, though I have no direct experience with them.
Another possibility is that the sewer vent is clogged, but that usually shows itself as slow flushing, rather than clogs, and sinks draining slowly and going glug-glug-glug. Usually, you have to attack this from on the roof.