Custom ESI block fails when submitting empty form field (?s= query string)

For some reason, our custom ESI block had trouble with some forms. I found some errors that I've been able to solve with some custom POST forms, but somehow I can't solve this one. When I use the regular search query string from WordPress, our custom ESI block just totally disappears. The HTML comments are there, no error is logged in PHP when we reset all caches...

I'll try to reproduce the issue in a fresh and closed environment to be able to send it to you, but so far it's on a whc.ca LiteSpeed enabled shared hosting setup for a private client that I can't disclose. More coming soon, but now gotta grab some sleep cuz I've been on that mystery for multiple nightly hours. 💀

No file, test, or entry point is named. Start by reproducing the custom ESI block with WordPress's ?s= search query and an empty form field, ideally outside the private LiteSpeed shared-hosting environment, then compare the rendered HTML and cache-reset behavior. Done means the custom ESI block remains present and renders correctly for that query.

Written by the indexing model from the issue text.