based on your measurements, this appears to be the same as the SewHandy (also made by Standard when owned by Osann).
Bad news - bobbins for this are very, very hard to find, and if you do you'll be in competition for them with the SewHandy crowd.
However, I did find that I have another bobbin that does fit in the case, and I can get it closed. It's a bit taller and does not have the beveled inner hole so it fits a bit looser. I've not sewn on the SH yet, but believe it came adjusted and ready to sew (but I'm not sure on that -CRS kicking in again).
BTW - older Standard bobbins do not fit, but they also look different so it's easy to tell.
Here are some older ones. They are from the machine I posted and a later model, and though the bobbins are a bit different, they are interchangeable.
This is from the SewHandy - please compare this to what you have to make sure it's the same. It measures about the same, but I use a micrometer to measure, and I don't think you did. I've got some that are about 1/32" different in some measures, but they won't fit. Interestingly - other than the inner hole being larger, this bobbin is the same width and height as the FW bobbin.
Here is the bobbin in the case - the unique part is the beveled edge to the inner hole - the case has two clips that slip into that bevel to hold the bobbin in place.
The closest match I have is the FreeWestinghouse (contemporary models). Here they are side by side
And in the case. It sticks out a bit and isn't super tight, but the case does close when put into the machine. It looks like a worse fit in the picture than it actually is. Shadows do that.
Next step will be to see if it will sew like that. If someone else has already tried this or has read about a substitute for the Standard made Sew Handy (not to be confused with the Singer toy of the same name), please share that.