Google Sheets, 44 bytes
=ifs(A1<2^8,1,A1<2^16,2,A1<2^32,4,A1<2^64,8)
Google Sheets uses IEEE 754 double-precision with a significand of 53 bits for pretty much everything, so cannot go all the way up to 64-bit unsigned.
The output format rules specified in the question are quite rigid. This alternative version outputs an array where the first true
value marks the minimum bytes required by the unsigned integer (2523 bytes):
=sort((A2<2^2^{3,4,5,6}))