letters = ["a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u",`
           "v", "w", "x", "y", "z"]

This method of writing the alphabet is very error prone. I would import string and use string.ascii_lowercase in place of letters. If you want to generate your own range of letters for whatever reason, I would write

letters = [chr(n) for n in range(ord('a'), ord('z') + 1)]

since there's then no danger of omitting or duplicating a letter.

password_length = 0
password_numbers = []
password_letters = []

These default values are never used. The defaults for password_numbers and password_letters don't make sense since those variables hold numbers. I would delete all three lines.

if not password_length_input.isnumeric():
    print(f"{password_length_input} is not a number, try again:")
    continue
else:
    password_length = int(password_length_input)
    print(f"Password length: {password_length}")

I would instead write

try:
    password_length = int(password_length_input)
except ValueError:
    print(f"{password_length_input} is not a number, try again:")
    continue
print(f"Password length: {password_length}")

while True:
    if password_numbers == password_length:
        ...
        break
    else:
        ...
        break

There is no sense in having a while loop here since you always break out of it on the first iteration.

range(0,password_numbers)

You can just write range(password_numbers).

password.append(random.randrange(0,9))

This will append a digit from 0 to 8 inclusive, never 9. If you want all ten digits you should write random.randrange(10). Or, perhaps better, use random.choice(string.digits).

password_string = ''.join([str(item) for item in password])

If you use string.digits then every element of password will be a character so you can simplify this to password_string = ''.join(password).

letters = ["a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u",`
           "v", "w", "x", "y", "z"]

This method of writing the alphabet is very error prone. I would import string and use string.ascii_lowercase in place of letters. If you want to generate your own range of letters for whatever reason, I would write

letters = [chr(n) for n in range(ord('a'), ord('z') + 1)]

since there's then no danger of omitting or duplicating a letter.

password_length = 0
password_numbers = []
password_letters = []

These default values are never used. The defaults for password_numbers and password_letters don't make sense since those variables hold numbers. I would delete all three lines.

if not password_length_input.isnumeric():
    print(f"{password_length_input} is not a number, try again:")
    continue
else:
    password_length = int(password_length_input)
    print(f"Password length: {password_length}")

I would instead write

try:
    password_length = int(password_length_input)
except ValueError:
    print(f"{password_length_input} is not a number, try again:")
    continue
print(f"Password length: {password_length}")

while True:
    if password_numbers == password_length:
        ...
        break
    else:
        ...
        break

There is no sense in having a while loop here since you always break out of it on the first iteration.

range(0,password_numbers)

You can just write range(password_numbers).

password.append(random.randrange(0,9))

This will append a digit from 0 to 8 inclusive, never 9. If you want all ten digits you should write random.randrange(10). Or, perhaps better, use random.choice(string.digits).

password_string = ''.join([str(item) for item in password])

If you use string.digits then every element of password will be a character so you can simplify this to password_string = ''.join(password).