Thanks for your ideas @Verhoeckx.
OhMyForm looks like a good candidate, worth considering.
You probably know this list: https://alternativeto.net/software/formspree-io/
Of those, FormSubmit, AirForm, Simple Form and Severless Form are candidates, imho.
There’s also SmtpJS that looks really interesting. I don’t know enough about smtp, so cannot judge.
Let’s find a good solution!