What is the correct way to write a follow-up email in case the first one ended up in spam folder?
Do not send a duplicate email. Send a follow-up email, with the previous one at the bottom (&quot;several weeks&quot; is already long enough without even an acknowledgement of receipt). Send it from your other address without mentioning the spam issue.
If your email was indeed lost to a filter, this resurrects it, without being an annoyance in the opposite case. Out of the 1% of people who will notice the different sender address (assuming the name you configured to appear is the same in both accounts), 90% will not care and 9% will guess why.
(If you are not sure how to write that follow-up email, it is a different question, that likely has many duplicates at workplace.se).