Is it possible to subscribe to the newsletter of a third-party service with email confirmation on the site?

Question

Email Marketing

Sorry for the chaotic title, but the deadlines are running out :)
The customer is going to use the SendSay mailing service for his site, but he does not deny that there may be another service in the future. He wants that when registering on the site, a person receives an email with a link leading to the site being developed to confirm the E-mail address (that it is real) (for example, https://my-site.ru/verify/ {unique-follow... ), but at the same time he also wants that when clicking on the same link, the person was also entered into the database of the mailing service (that is, he also gave consent to the mass mailing of letters from the service).
After thinking about it, I came up with two options for solving this problem:
1)When registering, a person is sent a letter from my server with a unique link that leads to the site being developed. The email address in the site database is confirmed, and then the server knocks on the API of the mailing list service and tells it that you need to add the data of such and such a person to the mailing list. But here problems arise: messages with a link end up in spam and people, as it were, do not confirm their consent to the newsletter from the service. The customer claims that such registration confirmation letters are usually sent not directly from the site server, but through mailing services, so they are not sent to spam.
2)Another option: when registering, a letter with a unique link to the user's mail is now sent from the mailing service. But here two other questions arise: how to send this most unique link (more precisely, a sequence) and how to mark in the database of your user that the email is confirmed? There are no Kalbeks at the service.
How are such registration systems usually implemented? I'm asking because of my inexperience. Can eat somebody who implemented it by means of sendsay. I would be very grateful for any tips.

Answer 1

such songs are definitely made with mailchimp and other sendpools
due to constantly changing policies - too lazy to figure out what is there and how it is now, but in general, if the right service is chosen, the design should work: all letters through the service, choose what you need via API