How can I safely get power into an outdoor enclosure from mains without a receptacle?
In the USA, all 120 volt branch circuits need to be run to listed boxes. The boxes must contain only listed receptacles, switches etc. You can buy boxes that are rated for outdoor use. They are equipped with covers that are large enough to plug in cords under the cover and have the cord exit the bottom with the cover closed. You can probably get away with running an extension cord from the receptacle to another box that houses the power supply. The 120 V conductors for the light can be attached to the back of the receptacle. You need to get wires out of the lamp post directly into the 120 V box or through a short piece of conduit.
What I am suggesting is to install a code compliant receptacle at a convenient location. Buy listed plug-in converters to supply the needed 5V and 12V. Enclose those in an enclosure that is large enough so that it won't overheat. Run an extension cord from that to the receptacle. Cut the molded receptacle from the end of the cord and replace it with a receptacle that screws together so that you can get the cord into the box through the entry gland. The DIY part will be a plug-in &quot;appliance.&quot; I don't think that electrical codes really regulate plug-in appliances. People are strongly encouraged to buy only appliances that are listed by a nationally recognized independent testing laboratory such as UL or ETL, but I don't think there is any way to enforce that. Packaging up some listed products is not equivalent to having the package listed, but there is no reasonable way to accomplish that. If you do a good job, it should be safe and not likely to generate any complaint.
The circuit going out to the lamp post needs to be GFI protected. You can use a GFI circuit breaker or make sure it is an extension of a GFI circuit or other outdoor receptacles.