Is there a Notix WordPress plugin?
No, and you do not need one. WordPress sends every email through wp_mail(), which hands the message to PHPMailer, and PHPMailer speaks SMTP. Any SMTP plugin, or a ten-line must-use plugin on the phpmailer_init hook, points that at the Notix relay. From there the message is the same tracked send the API makes. A dedicated plugin would only be a settings screen for the same four fields.
Which settings do I put in WP Mail SMTP or FluentSMTP?
Pick the "Other SMTP" mailer. Host smtp.usenotix.dev, port 465 with SSL encryption (or 587 with TLS), authentication on, username notix, and any Notix API key as the password. Set the From email to an address on a domain you verified in Notix and turn on "force from email" so plugins cannot override it with an unverified one.
Where should the API key live?
Not in the database if you can help it. WP Mail SMTP reads WPMS_SMTP_PASS and the other WPMS_* constants from wp-config.php when WPMS_ON is defined, and greys the fields out in its settings screen. FluentSMTP offers the same choice when you save a connection: keep the credentials in the database or in wp-config.php constants it names for you. The mu-plugin on this page reads a constant or an environment variable. Either way, create a key just for the site so revoking it does not touch anything else.
Why does WooCommerce or Contact Form 7 stop sending after I switch?
Almost always the From address. The relay refuses mail from a domain you have not verified in Notix rather than sending it unauthenticated. WooCommerce uses the "From" address under WooCommerce, Settings, Emails; Contact Form 7 uses the From header in each form's Mail tab, and the WordPress default is wordpress@ your site's hostname. Set all of them to a verified domain, or turn on your SMTP plugin's force-from option so every message leaves under the address you configured. Put the visitor's address in Reply-To, not From.
What do I get that wp_mail() alone does not?
A record. Each message shows in the Notix dashboard with delivered, bounced or complained status, the same events reach any webhook you register, and an address that bounced or unsubscribed is suppressed automatically on the next send, whether it came from a password reset, an order email or a form. wp_mail() on a bare host gives you a boolean and no idea what happened after.
Does this cover WooCommerce order emails and password resets?
Yes. Everything WordPress sends goes through wp_mail(): new-user and password-reset mail, comment notifications, WooCommerce's order, refund and account emails, and whatever your form, membership or booking plugins send. If a plugin bypasses wp_mail() with its own mailer (rare, and its settings will say so), point that mailer at the same host and login. Marketing mail to a list belongs on Notix campaigns rather than in a WordPress loop.