How to fix broken styles in the Amasty's «Advanced Search» module after upgrading it to 1.12.x?

Step 1

Downgrade the amasty/xsearch Composer package to the 1.11.2 version.

Step 2

Downgrade the module’s version in the Magento’s database:

UPDATE setup_module
	SET schema_version = '1.0.1', data_version = '1.0.1' 
	WHERE 'Amasty_Xsearch' = `module`

Step 3

Re-compile the code and re-deploy the static content.