Hello Jan,
Thanks for the very precise report. We reproduced the issue on a local Joomla 6.1.0 + HikaShop main + JCE installation, the failure is exactly as you describe: PluginHelper::importPlugin('search') tries to parse our two search plugin files before any code path that would have aliased the legacy JPlugin / JPluginHelper / JRegistry names has run, and class loading fatals at the class declaration line.
Our fix is in our next release. Rather than switching the parent class to Joomla\CMS\Plugin\CMSPlugin (which would break Joomla 3 and Joomla 4 environments where the namespaced class is not always autoload-resolvable in plugin context), each search plugin now declares the three aliases (JPlugin, JPluginHelper, JRegistry to their modern namespaced equivalents) inline at the very top of the file, gated by class_exists($legacy, false). The class declaration below then always parses, regardless of whether compat6 has fired, whether its classes_aliases parameter is on, or whether HikaShop's helper.php has been loaded yet in the request. Behaviour on Joomla 4 and 5 is unchanged (the existing aliases are detected and the inline ones are no-ops).
A package containing the patch has just been uploaded; please update HikaShop to confirm it resolves the issue on your end.
One small thing if you have a moment: could you share the full stack trace from the 500 you saw? Your report mentions "all ours" in the page-URL field and we want to make sure the failing call path on your sites really is the JCE Insert/Edit Link one we reproduced and not a second caller of PluginHelper::importPlugin('search') that we have not accounted for. On a stock Joomla 6 installation com_search no longer exists and JCE, which is not included in Joomla by default, is the only place we found that still uses the search plugin group (and that's why we never changed these plugins because they are meant to be used only on Joomla 3 / 4 and should not be called normally on Joomla 6). If a third extension on your stack is also calling it (or if it is firing on every front-end render rather than only when the link picker opens) the trace will tell us.
Thanks again for the report and for offering to test, very much appreciated.