My question is this: Is there a problem with putting this kind of oil in my Troy-Bilt PowerSmart lawnmower? The specifications call for SAE 30, but I was wondering if SAE 10W-30 would be good enough and not give me any trouble with the lawnmower engine.
SAE-30 is specified as the lawnmower is basically used in summer.
So, using SAE10W-30 will be fine as it has the equivalent hot specification ie the "30" part.
The user manual on the OP's web page actually recommends 10W-30 oil, for use in all reasonable weather conditions. (I suppose some Canadians might want to mow their lawn when the temperature is below 0F and should use 5W-30 instead, but I wouldn't call that "reasonable"!)
When all else fails, read the documentation: https://images.homedepot-static.com/catalog/pdfImages/21/215ed4a6-3a98-4685-a7ea-5d5487a1eb2f.pdf Page 12.