Not for pythonicism, but out of curiosity, I quickly made up a benchmark and compared three variants:

1. My version I currently use in a web stats backend

2. Something I found in a C++ SO post (https://stackoverflow.com/questions/45225089)

3. Is #2 on steroids: Roll out bit by bit. And it's the fastest one, at least on my machine (i7-12700, Python 3.13).

from datetime import datetime as dt

# This is my version currently in use (31 is to fit cnt2)
def cntz(i):
    if i == 0: return 31
    z = 0
    while i > 0 and i & 1 == 0:
        z += 1
        i >>= 1
    return z

# The C++ one from https://stackoverflow.com/questions/45225089,
def cntz2(i):
    z = 0
    if i & 0xFFFF == 0:
        z += 16
        i >>= 16
    if i & 0xFF == 0:
        z += 8
        i >>= 8
    if i & 0xF == 0:
        z += 4
        i >>= 4
    if i & 0x3 == 0:
        z += 2
        i >>= 2
    z += (i & 1) ^ 1
    return z

# My try: Unroll it bit-by-bit. Stops at 23 to fit the 10M test
def cntz3(i):
    if i & 0x00000001: return 0
    if i & 0x00000003: return 1
    if i & 0x00000007: return 2
    if i & 0x0000000f: return 3
    if i & 0x0000001f: return 4
    if i & 0x0000003f: return 5
    if i & 0x0000007f: return 6
    if i & 0x000000ff: return 7
    if i & 0x000001ff: return 8
    if i & 0x000003ff: return 9
    if i & 0x000007ff: return 10
    if i & 0x00000fff: return 11
    if i & 0x00001fff: return 12
    if i & 0x00003fff: return 13
    if i & 0x00007fff: return 14
    if i & 0x0000ffff: return 15
    if i & 0x0001ffff: return 16
    if i & 0x0003ffff: return 17
    if i & 0x0007ffff: return 18
    if i & 0x000fffff: return 19
    if i & 0x001fffff: return 20
    if i & 0x003fffff: return 21
    if i & 0x007fffff: return 22
    if i & 0x00ffffff: return 23
    return 31

input = range(10000000)

for f in [cntz, cntz2, cntz3]:
    t0 = dt.now()
    output = list( f(_) for _ in input )
    print(f'{(dt.now()-t0).total_seconds():.3f} {output[:33]}')

Output

1.797 [31, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5]
1.917 [31, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5]
0.873 [31, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5]