Over the last few months we have noticed a "septic" smell progressively getting worse in one corner of our basement that also travels through our air intake vent into the house. This seems to happen when we do laundry, dishes or baths. I have had my tank pumped regularly. I do have a sump hole in this corner of the basement, but have not noticed a smell coming from the hole.

Could a bad seal on the toilet (first floor - opposite side of house) attribute to the foul smell in the basement?

I appreciate all input - thank you

If you have any floor drains in the basement be sure to pour some water in each. If the drain is trapped it could evaporate its water seal over time. If that doesn't work you may need to rod your main vent stack that goes through the roof. You smell the gas while washing because the draining water is pushing the fumes and they aren't going up the stack like they should. Tiolet seal is a possibility but slight compared to the two suggestions.
Please rate my answer so I'll Know if I helped you. Good luck