What is the role of 曾经 in this sentence? 欧盟委员会曾经宣布，将暂时维持对中国皮鞋的反倾销税措施。

Can I write： ‘欧盟委员会宣布了‘ or ‘欧盟委员会宣布过‘，or even ‘欧盟委员会曾经宣布过‘instead？ I mean, is it a past tense marker here, or does it mean 'once'?
'曾经' means 'once' here. This word is used when you talk about some situation that has occurred or has been experience before. I don't find this case weird at all.

'宣布过' is similar to '曾经宣布', actually '曾经宣布过' is also good here.

'了' is different. It stresses on the fact that some action or behavior has been finished.

By the way, there's no 'tense' in Chinese. You may say that these words are related to the past, so the sentences that have them are usually translated into past tense.