If i understand your description of what you do correctly, then clicking the email links in incognito mode does not help you in any way. The long weird url is almost always a tracking link unique to the specific email that you received. Clicking it verifies that you received and read the email sent you your email adress, no matter where you click it
When I decide to click on the link then I accept the other side will know I clicked on that URL. What I tried to say was that I am always a bit worried that by clicking on a link there will be a chain of redirects or some click-jacking technique (or anything else) that in result will take over one of my accounts which I'm keeping logged in on my main browser (i.e. google, or LinkedIn)
I'm not particularly sure I understand. You're worried that because the URL is long that it might somehow take over your google account? I'm not quite sure I understand the correlation between "long URL" and redirects/clickjacking.
Looks like I structured what I tried to say in wrong way, sorry about that, English is not my mother tongue and sometimes I try to say too much in one sentence. I generally don't trust hyperlinks sent to me when pointing at source I have never seen before. I open such URLs in private session.