This seems an issue related to an extension that uses the browser.i18n API to localize its options page text (which is what this extension is doing that the other tested extensions were likely not doing). It looks that the i18n API is failing to retrieve the expected localized strings if the options page is open while the extension is being restarted (which happens automatically every time the private browsing access for that extension is toggled).
Bug 1540106 Comment 1 Edit History
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This seems an issue related to an extension that uses the browser.i18n API to localize its options page text (which is what this extension is doing that the other tested extensions were likely not doing). It looks that the i18n API is failing to retrieve the expected localized strings if the options page is open while the extension is being restarted (which happens automatically every time the private browsing access for that extension is toggled). The issue is not specific to "toggling the private browsing buttons", e.g. it can also be reproduced by disabling and re-enabling the addon using the related button in the extension details page (which it is also useful to determine if this is a regression or not, because it will allow to verify if the issue was already before Firefox 67, where the extension "private browsing" buttons were not available yet).