Rabbi Joshua Berman addresses some of the issues that you raise in his book Ani Maamin.
Rabbi Berman brings academic research to support the idea that some language forms, rules and practices found in the Torah were culturally appropriated, some from Egypt. For example (and not relating to the OP's question directly), the term "strong hand and outstretched arm" found in the Torah is a phrase used only regarding the Exodus from Egypt. Rabbi Berman also shows that it is a common term used throughout Egyptian writing when referring to some action carried out by the Pharaoh. Although this cannot be known, the phrase could have been appropriated into the Torah as a direct challenge to the Egyptian leadership who were the most powerful civilization of the time in the region. There is good reason to do this as will be explained.
Specifically referring to the Mishkan, Rabbi Berman says that scholars debate its origin. However, some find stark similarity to the battle encampment of Ramsesses II at the Battle of Kadesh. Here is an Egyptian inscription of the encampment at the battle of Kadesh (at Abu Simbel):
And here is a close-up of the military tent of Ramesses II, see this website:
Rabbi Berman notes that the ratio of the dimensions of the Mishkan are the same as the dimensions of the military tent of Ramesses II. They are both 1:2 for the "holy" outer chamber and 1:1 for the "holy of holies" inner chamber.
There appears to be resemblance between the two. The website above suggests that the two winged figures in Ramesses's inner chamber are that of the god Horus (often depicted as a falcon with wings) and was a symbol of kingship. The two winged figures face towards the cartouche of Ramesses II, as his protector. This resembles the cherubim of the ark facing each other.
This motif of the pharaoh being protected from both sides is not unique to this hieroglyphic relief, but was relatively common. For example see this rendering of Ramesses III flanked by the gods Horus and Seth:
With regards to why the Torah would appropriate this motif (if this is what happened), there are plenty of examples of similarities in practice between Jewish and ancient cultures, see here for example.
I would like to note that this particular connection between the mishkan and the encampment of Ramesses II is a very recent one, I think Rabbi Berman says it was from research in the 1930's, as the discovery and scholarship of Egyptian literature advanced. However, a similar line of thought regarding appropriation of extent religious practices can be found in the Rambam. For example see the Moreh Nevuchim Part 3, 32 where the Rambam writes about why sacrifices were incorporated into the Torah despite it merely being a ritual practice of various religions of the time. Here the Rambam is telling us why it would seem, at face value, strange to incorporate a ritual practice of another civilization, but shows that there is good reason in doing so.
I would really recommend reading the whole passage from this Rambam to get the idea of what he is saying and suggesting. Basically, in order to bring a people towards Godly service of Hashem we cannot, with a single miracle, get them to change; it is a process that must be mediated and has a historical context. The incorporation of sacrifices was a necessary incorporation into the Torah to redirect the people away from idolatry.
The Rambam continues to explain how sacrifices are not the primary objective and yet they are incorporated into the Torah (ibid.):
"As the sacrificial service is not the primary object [of the commandments about sacrifice], whilst supplications, prayers, and similar kinds of worship are nearer to the primary object, and indispensable for obtaining it, a great difference was made in the Law between these two kinds of service."
As I mentioned, this last part about sacrifices does not answer the question of why the Mishkan bears resemblance to the military encampment of Ramesses II or whether it was appropriated. This just goes to show that, according to the Rambam, at least sacrifices were appropriated into the Torah for a higher purpose of leading the people away from idolatry. By extension, it could be that other aspects of the Torah were incorporate from other religions and/or civilisations of the time as part of the broader purpose of turning the people away from idolatry using familiar practices of the time. Since the Rambam didn't know about the Egyptain inscriptions we cannot know how he would react to it. However, this gives us a glimpse into his approach regarding appropriation of extent practices.
