Possibly the handlebars/fork should be turned around, looks like the handlebar neck portion slightly interferes with the seat spring the way it currently is in the photos you posted. Once the handlebars are turned around, if the curvature of the handlebars does not seem correct, is it possible they are simply bent maybe from falling over? Many Velocipedes from this era had straight handlebars but that is not to say your bars are incorrect as curved. I'm suggesting that you look at your bars very carefully with that thought in mind and make a careful assessment based on your Velocipede.
This Picking advertisement shows the handlebars turned the same direction as the Henry Ford collection Pickering and the handlebars appear to be straight.
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This Pickering from the Metz collection shows the handlebars turned the same direction as yours and a similar curvature but possibly it is also bent and turned incorrectly?
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I'm not sure what the correct answer is regarding the handlebars, you will need to make that determination based on what seems correct after turning it both directions and determining if the curvature of your handlabars was manufactured that way or possibly bent by accident or on purpose at some later time.
Keep in mind, the Pickering examples I have presented are just that, examples. I am not convinced your Velocipede is a Pickering. Fitments such as bearings could be ordered from catalogs during this time. Velocipede manufacturers were like bicycle manufacturers today. They may produce a frame or purchase one from a blacksmith, purchase bearings from a catalog, purchase wheels from the local wheelwright, and purchase a saddle from the local leather tack shop. Velocipede manufacturers basically never produced every component of the entire machine. What is very likely is that the manufacturer of your Velocipede copied a Pickering or possibly Pickering copied your manufacturer. They may have even been acquaintances producing similar looking machines because of the availability of parts such as using the same bearings from a bearing manufacturer.