hard to start after fillup

I bought a 2008 Accent GS in late August 2022, a well cared-for one-owner car; but every time I fill the tank at a gas station, it takes about twenty seconds of cranking to start, and then will not idle properly until a few minutes later. Otherwise, starting is very fast, and idle is fine. Two people have told me it is a fuel-cap problem (?) and I wonder if that is possible. I plan to buy a new fuel cap to test that idea; but does that seem reasonable?

 

Did you get a new fuel cap? Just wondering how this worked out for you.

 

I did get a new fuel cap, also put injector cleaner into the tank, but the problem yet persists. I asked my brother about it, and he said it may be a stuck valve in a venting line, so I need to take it to my friendly local shop.