Imperial Germany, not so much. The Germans were much more interested in forging their identity, rather than in adopting another people's. A lot of this apprehension for complete identification with Rome came about as backlash against Napoleon, who was the embodiment of a much more Roman zeitgeist as France experienced during and after the Revolution. Napoleon's own desires to assimilate other peoples into his empire ended up simply causing those peoples to grasp more tightly into what was "theirs."

The Hermmansdenkmal in NRW, the Walhalla in Regensburg, and the Niederwalddenkmal are all examples of a supposed Romantic German identity. Although they utilized Classical art and motifs for their aesthetics, they were not intended to showcase Classical tropes or elements of Classical culture outside of their aesthetic purpose. The Hermmansdenkmal was actually a portrayal of Arminius, the Germanic chieftain who annihilated three Roman legions. Furthermore, the statue is pointing to France, signalling continued German animosity against the Latin peoples, represented by France. Walhalla is another example: a neoclassical temple utilizing Nordic motifs. Essentially, through these examples I'm trying to say that German identity was formed out of a Romantic backlash against the Neoclassical Napoleonic Empire, which would rule out being a Roman successor since they were opposing the Roman successor.

I wish I could say more about Romanov Russia, but I really don't know much in that field.

It's a stretch. I wouldn't say that the Muscovy/Russia saw itself as a new Byzantium, instead that they were a new Rome in the same way Byzantium had claimed itself to be. This is a pretty decent primer on the Third Rome ideology.

The Russian Orthodoxy, after the fall of Constantinople, considered itself the last true Christians. It's not that the Catholics were also-Christians-who-we-disagree-with, they were apostates within that theology. If Byzantium had authority to the Russian Orthodox, it was only because they derived that authority directly from Rome.

Now, you could make a claim about derived legitimacy. The German Empire, however, derived its legitimacy much more directly from the Holy Roman Empire. The Russians make their claim effectively by default after the conquest of the Byzantines.