There'll never be any 'final' answer on any matter, so if anyone would like to contribute further posts on what happens to embassies during times of war, don't let my skill at copy-paste stop you from putting fingers to keyboard! For the meantime, OP, we do have some previous posts examining some situations where this happens.

• u/Georgy_K_Zhukov looks at the British mission to Germany, and in conjunction with u/indyobserver, have some interesting reading on the US embassy in Japan in this most excellent thread.
• u/kieslowskifan also has a bit on the US embassy in Japan here.

One more case study in the next post because argh tag limit.