Excellent, however less stars because, as others already commented, search customization is not available in the extension, which is necessary if cookies are deleted at restart/not saved at all.

Please add this functionality to the GUI of the add-on. Thank you.

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Here is a way to do it manually, however with many caveats (no updates, search string not changeable, modifying the extension):
1) create a searchstring on https://www.startpage.com/search/settings
2) copy the string starting with "?prfh="
3) install the startpage add-on, close Firefox and navigate to your profile folder where the extensions are stored (usually something like: "userdata directory"/mozilla/firefox/"profilename.default"/extensions )
4) copy {20fc2e06-e3e4-4b2b-812b-ab431220cada}.xpi and open the copy with an archive program (alternatively rename it to .zip, then open)
5) open manifest.json
6) Look for the line "search_url": and delete everything after "dsearch?query={searchTerms}&" and add your personal string starting with "?prfh=" to it.
7) the string should look similar to this: https://www.startpage.com/do/dsearch?query={searchTerms}&prfh=enable_stay_controlEEE0N1NsuggestionsEEE1N1Ngeo_mapEEE1N1Nwikipedia_iaEEE1N1Nother_iaEEE1N1Ndisable_open_in_new_windowEEE0N1Ndisable_video_family_filterEEE1N1Nenable_post_methodEEE1N1Nenable_proxy_safety_suggestEEE1N1Ndisable_family_filterEEE1N1Nconnect_to_serverEEEeuN1NsslEEE1N1Nlanguage_uiEEEenglishN1NlanguageEEEenglishN1Nwt_unitEEEcelsiusN1Nnum_of_resultsEEE20N1Nlang_homepageEEEs/default/en/
8) save it (rename the zip to xpi again)
10) start Firefox and uninstall the startpage add-on


Technically we have a working add-on now. However Firefox disabled unsigned add-ons for security reasons. So the add-on can't be installed.
9) navigate to "about:debugging#addons" and click "Load temporary Add-on". Now you can add your newly created extension and see if you did everything right.
10) However after each restart of Firefox the extension will be deleted. There are multiple ways to prevent this, however none is really secure/ideal. I chose to upload the new add-on as private add-on here https://addons.mozilla.org/en-US/developers/addon/submit/ . This signs the add-on officially by Firefox and only let's you download it instead of making it available for others too.
11) Disable updates to the extension. (As nothing got modified in the package except the url, i am unsure how the add-on will behave if there is a new update from startpage. Either it won't install or the private search string will probably be deleted.)
12) Check regularly for the official extension to be updated and include this functionality. This workaround is not ideal, as it is unfair towards the developers to use a modified version of their extension