Yes, the hub is identical
Same 5x112 PCD and same 66.6 mm centre bore: wheels from Mercedes E-Classe W213 bolt on and centre on BMW 3 Serie G20-G21 without rings. You still need to check the offset and tyres, detailed below.
≈: width estimated from the original tyre size.
Wheel by wheel: offset and tyres
Each original wheel from Mercedes E-Classe W213 is compared with the one from BMW 3 Serie G20-G21 of the same diameter: how much closer the wheel gets to the shock absorber or how far it sticks out of the wheel arch, and whether the tyre keeps the same overall diameter.
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≈6.5Jx16 ET32 · 205/65R16 — Check on the car
Compared with the original 6.5Jx16 ET22 on BMW 3 Serie G20-G21: shock absorber side +10 mm, wheel arch side −10 mm, tyre diameter +3.1 % : fit it with the original tyre size of BMW 3 Serie G20-G21 (205/60R16), not that of Mercedes E-Classe W213.
Comparison for guidance only (estimated width). Check in detail
Before fitting the wheels
An identical hub is not enough: offset, width and diameter change the position of the wheel, and larger calipers can touch a smaller wheel. Original wheels often use bolts or nuts with a specific seat: keep the fixings intended for the wheel, with the thread of BMW 3 Serie G20-G21 (M14x1.25), tightened to the torque shown on its vehicle page. Finally, check that the size is among the approved fitments for your vehicle. This comparison is for guidance only: have the fitting approved by a professional.
And the other way round: wheels from BMW 3 Serie G20-G21 on Mercedes E-Classe W213?