Thank you for the detailed description, it helped me a lot!
It appears that the override option is causing the problem. I guess maybe a query variable used by the theme or within the code might be the same as the one that the search uses, and probably causing the 404 error. Or there might be another override active from a different plugin, I'm not sure.
I have turned off the override on the General Options -> Behavior panel, I believe it should redirect correctly now.
If you want, I can investigate the issue in more details. In that case please update your ticket with FTP details as well.
I hope that solved the problem!Best,
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