It worked well in the past with Search module. However, now we get error "WebAssetManager is locked, you came late" after switching the "Search" module in the code from Search module to Smart Search module. Joomla cache is disabled.
Can you give me (super) admin and (s)ftp access so I can take a look?
And tell me where you have placed the {module} tag, and on what url I can see/reproduce the issue.
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Weird, I cannot reproduce this behavior on my own setup.
It could be due to the template. I see you are using Page Builder. That could be handling things differently.
Also you have a lot of other plugins installed.
See if you can reproduce the issue on a clean Joomla setup, not using Page Builder.