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Can anyone tell me if there is supposed to be spring attached to the choke lever. Mine hasn't one and it doesn't have any way to assist back to open position
other than just gravity.

There is a tiny clock spring between the carb and the plate on the top of the choke shaft that the control rod links into

Would you direct me to a vendor with a part #

https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/briggs-stratton/400000-699999-series/445500-to-445599/445577-0026-g1/carburetor-fuel-supply

Part 217 in the diagram above from the vendor above.
Check the freight it will most likely be a lot more than the $ 5 part in which case order on from your local B & S dealer