Tested with 0.11.1 (fabric 1.19.2). Not Enough Animations has a custom crawling animation which does not show up at all using your mod, neither using the keybind nor using a trapdoor to crawl.

Since v0.14.4 (MC 1.21.1, 1.21.4), it is possible to disable crawl animation replacement, via options.
2.5 years passed, phew..

lmao only took a lil bit