It seems like the consensus among various commentators is that this Passuk isn't understood to mean that Hashem is saying that the people will have have some physical power that enables them to literally accomplish anything they attempt to do. Rather, this statement is meant to reflect a mindset and potential results that come about due to having a shared language.
The commentator who most explicily explains in this manner is the Ibn Ezra, who writes:
וזה הטעם אם אעזבם יחשבו שיוכלו לעשות כל חפצם
Loosely translated as if humanity was left to their own devices, they will believe (emphasis mine) that they could do whatever their heart desires.
Sforno says a similar idea, that the Passuk is expalining how humanity will respond to uniformaity in language. Quoted in full below, the gist of the idea is that the uniformaity in language will be a strong obstacle in preventing humanity from believing in the single all-powerful G-d:
ועתה לא יבצר מהם אם כן אין מונע להם מהשלים כונתם ותהיה אותה עו''ג אשר
יבחרו כללית לכל מין האדם ולא יפנה אחד מהם לדעת את הבורא ית' ולהבין כי
יוצר הכל הוא. והפוך זה יקרה כשתהיה מחלוקת בענין האלהות כי כל אחד יחשוב
שיש אלהי האלהים שכל האלוהות מסכימי' לדעתו ובו ישלם סדרם וסדר המציאו'
כאמרו כי ממזרח שמש ועד מבואו גדול שמו בגוים:
ועתה לא יבצר מהם, in view of these circumstances, if left alone, they
would complete what they have set out to do, so that this form of
idolatry they have agreed on would henceforth be something embraced by
all of mankind. Not a single one of them would turn to the Creator of
the universe and realise that He, and He alone, is the Creator of the
entire universe. On the other hand, the opposite will occur if discord
will break out among them regarding the supremacy of any of the
deities versus the competing ones. In such a scenario, every nation
would believe that there is one deity that is superior to all the
various national deities, whose concern is only with the particular
nation worshipping that deity. All the minor deities would have to
subordinate themselves to the power of that super-deity. The prophet
Maleachi 1,11 expresses this in the following words: ”for from where
the sun rises to where it sets, My name is honoured among the
nations;” כי ממזרח שמש ועד מבואו גדול שמי בגוים.
Lastly, Rashi explains this as a sort of rhetorical question being asked by G-d. G-d seems to be saying that it would be unnacceptable for humanity to be allowed to continue on its' current path without any intervention.
לא יבצר מהם וגו' לעשות. בִּתְמִיהָ. יִבָּצֵר לְשׁוֹן מְנִיעָה,
כְתַרְגּוּמוֹ; וְדוֹמֶה לוֹ יִבְצֹר רוּחַ נְגִידִים (תה' ע"ו):
לא יבצר מהם וגו' לעשות This is a question (although the ה which
introduces an interrogative sentence is absent): SHALL THEY NOT BE
RESTRAINED FROM DOING WHAT THEY IMAGINE TO DO? The word יבצר means
“restraining”, as the Targum understands it; a similar instance is,
(Psalms 76:13) “He restrains (יבצור) the spirit of princes”.