For the classic site, you could hide the recycle bin from navigation bar of a particular page with following CSS codes in the script editor web part.
<style type="text/css">
#sideNavBox a[title="Recycle Bin"]
{
display:none!important
}
</style>
For the modern site, activating the "SharePoint Server Publishing Infrastructure" feature is the only available OOTB option. Because that's by design.
As a workaround, you could install modern script editor web part, then use provided CSS codes in the modern script editor web part.
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