I don’t think your assumption on how well I understand how the professional world works is correct.
I understand very well that signing any NDA is by no means “zero risk”, it has a definite risk attached to it. Declining it is costly in some way, but also has definite advantages.
I also understand that very rarely is the phrasing ever “this conversation will be off the record”, but rather some phrasing including the specific topics that may not be shared, like you say for example, product details. Blanket phrasings like this are always very sketchy.
The functionality in this script is indeed only possible as an addon or userscript. Browsers specifically spent a lot of work trying to make it impossible for one site to get any information about which other sites the user visited, and for good reason. Just imagine the phishing this would allow if it were possible.
That said, there could of course be an official lemmy browser addon/userscript for this functionality. But it definitely wouldn’t be baked into the sites themselves.
Because idk if you noticed, but this script actually rewrites all links everywhere, so for example even if you get a result to some lemmy instance on duckduckgo, the link on duckduckgo itself will already point to your instance. Please tell me how that would be possible without an addon/userscipt :D