Transformer won't work for US plug

The socket on the transformer is a "CEEform" or "Commando" socket (they are two names for the same thing). It's a widely used international standard, but is completely incompatible with the standard German or French plugs.

You would need to buy or make an appropriate adaptor to fit your US plugs. Or take off the US plugs and fit CEEform ones instead.

Note that yellow plugs/sockets are specifically intended for 110V. Other colour plugs will not fit, even if they are the same size.

Wrong adapter

Your problem is basically entirely that you have the wrong adapter. Your transformer is a UK worksite transformer that outputs two 55V legs with an inaccessible center-tap for the grounded neutral, and thus uses IEC 60309 pin and sleeve (also known as "CEEform" or "Commando" in the UK) type connectors as they are rugged and weather-resistant. These are not intended to mate with the Schuko plug on your current adapter, though, so you'll need to get or fabricate (using a short length of appropriate cordage as a go-between) an adapter from the appropriate pin-and-sleeve plug to a NEMA 5-15 cord cap and use that instead.