To what extent is the prayer "O Allah, bless our Master Muhammad an innumerable number of times, as much as what is in Allah’s knowledge, with a perpetual blessing, as perpetual as the persistence of Allah’s dominion" valid? Is it an innovation (bid‘ah)? And does it entail the reward of six hundred thousand prayers for the felicity of both abodes, as mentioned by Sidi Ahmad al-Sawi?

It is permissible to invoke blessings upon the Prophet, peace and blessings be upon him, with any formula that does not include a sharia-prohibited element. However, it is preferable and better to restrict oneself to the formulas that have been authentically transmitted from him, peace and blessings be upon him; such as the Ibrahimiya formula, based on his saying, peace and blessings be upon him: "Say: O Allah, bless Muhammad and the family of Muhammad, as You blessed the family of Abraham, You are indeed Praiseworthy, Most Glorious." Scholars have used his teaching of this method, peace and blessings be upon him, as evidence that it is the best way to invoke blessings upon him.

As for the formula mentioned in the question ("O Allah, bless our master Muhammad, as many times as there is in the knowledge of Allah, a blessing that is everlasting as long as Allah's dominion lasts"), it has not been authentically transmitted from the Prophet, peace and blessings be upon him, and scholars have described it as an innovation (bid'ah). Furthermore, the reward claimed for it is baseless.