I don’t know how your sink in this main toilet is vented, but it likely has a studor vent under the sink. If it does, this vent could be venting sewer gases into your bath area. To eliminate the possibility of a bad vent, put a ziplock bag over it with a rubber band. If the smell goes away, replace the vent. They are available at the big box stores or any plumbing dealer.
Otherwise, I have no idea about the possible toilet problem.