Isn't that the right way around? Embassies in foreign countries need more protection than buildings in your own home country?

I think you should read up on how western countries typically prefer to have very light visible security in front of buildings like these. It sends a message of non-approachability if you have heavily-armed forces out front, which politicans don't like.

I'm assuming a similar security plan is in place in e.g. European countries' parliaments; extracting the high value targets is P1. The building is just a building; if it's damaged it can be repaired. And killing a bunch of people defending a building is a political no-go.

None of this applies to an embassy.

I'm pretty sure, almost every US Embassy, not just in Amsterdam, is better protected.

Apparently there was a joke going around latin america twitter that the coup failed because there is no US embassy in DC to support it.