Is Bidʻah (innovation) in religion, as evidenced by the Bilal's act and the addition of "Our Lord, to You be all praise, abundant praise," and the legitimacy of the Adhan (call to prayer) from a vision?

The era of the Companions is not like any other, because the Prophet's — peace and blessings be upon him — approval of their actions during the time of legislation indicates the infallibility of that era from error. The proof lies not in their mere actions, but in the approval of the Law-Giver (the Prophet) for them. These actions are called Sunnah (definition) Taqrīriyyah (tacitly approved Sunnah).

However, this does not imply the permissibility of innovation (bid'ah), as the Prophet — peace and blessings be upon him — did not approve some of the Companions' ijtihād (independent reasoning) in matters of worship. The principle is adherence to the Sunnah of the Prophet — peace and blessings be upon him — without excess or negligence.

The actions of the Companions that the Prophet — peace and blessings be upon him — did not legislate himself are not considered a recommended Sunnah. Rather, they are matters in which ijtihād is permissible or their doer is not to be denounced, as long as they are not adopted as a regular Sunnah.

As for the examples mentioned in the question, such as Bilal's action and the Companion's saying after rising from rukūʿ (bowing), they are not innovations because they fall under a general principle, which is the virtue of remembering Allah. There are general texts that encourage the remembrance and praise of Allah.

As for the legislation of the Adhan (definition) (call to prayer), it was not implemented based on the dream of Abdullah ibn Zayd, but rather by the command of the Prophet — peace and blessings be upon him — who affirmed that it was a true dream.