If the program or tool Email newsletter/marketing for a site not done in any CMS like Shopify/Wordpress etc?

Looking for a tool, a tool where I could just paste the script or use their programmed form so that the visitors of my site can subscribe to news and their email has already been preserved in the dashboard of the platform of the instrument itself (i.e. the platform that the script suggests), where I wish I could them all at once to send all my news emails. I have a website in pure html/js.

Klaviyo, Omnisend, etc. are not suitable since they only E-Commerce platforms and Wordpress sites, and with their API to suffer I don't want to. I only need subscribe and save these clients in my dashboard (actually not mine and the company that offers me this service).

Would be glad if someone familiar with this topic.