Is it a vampire number? Repost and improvement of this challenge from 2011
A vampire number is a positive integer \$v\$ with an even number of digits that can be split into 2 smaller integers \$x, y\$ consisting of the digits of \$v\$ such that \$v = xy\$. For example:
$$1260 = 21 \times 60$$
so \$1260\$ is a vampire number. Note that the digits for \$v\$ can be in any order, and must be repeated for repeated digits, when splitting into \$x\$ and \$y\$. \$x\$ and \$y\$ must have the same number of digits, and only one can have trailing zeros (so \$153000\$ is not a vampire number, despite \$153000 = 300 \times 510\$).
You are to take a positive integer \$v\$ which has an even number of digits and output whether it is a vampire number or not. You can either output:

Two consistent, distinct values
A (not necessarily consistent) truthy value and a falsey value

For example, &quot;a positive integer for true, 0 for false&quot;



You may input and output in any convenient method. This is code-golf, so the shortest code in bytes wins.
The first 15 vampire numbers are \$1260, 1395, 1435, 1530, 1827, 2187, 6880, 102510, 104260, 105210, 105264, 105750, 108135, 110758, 115672\$. This is sequence A014575 on OEIS. Be sure to double check that your solution checks for trailing zeros; \$153000\$ should return false.
Husk, 18 17 14 13 12 bytes
Edit: -3 bytes, and then another -1 byte, thanks to Leo, and -1 byte thanks to inspiration from pajonk's R answer (3rd edit)
€¹mΠ†dm½f→Pd

Try it online!
Outputs nonzero integer if it's a vampire number, zero otherwise.
Commented penultimate version:
€¹                  # index of input if present, zero otherwise, in
  mΠ                # products of each element-pair
    †d              # combining digits as a number from
         m½         # first &amp; second halves of
           P        # all permutations of
            d       # digits of input;
      f             # and filtering only element-pairs for which
       ṁ→           # sum of last digits is nonzero