Is SSL necessary when sending password to a API from a server?

Question

I have bought a online service which allows me to send SMS messages by making a call to the provider's SOAP-API.

This is the WSDL I need to send a message:

<?xml version="1.0"?>
<soap:Envelope
    xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/"
soap:encodingStyle="http://www.w3.org/2003/05/soap-encoding">
    <soap:Header>
        <authenticate_user
            xmlns="http://www.example.net/ns/">
            <username>MY_USERNAME</username>
            <password>MY_PASSWORD</password>
        </authenticate_user>
    </soap:Header>
    <soap:Body>
        <send_sms
            xmlns:m="http://www.example.net/ns/">
            <user_id>???</user_id>
            <from>???</from>
            <to>???</to>
            <message>Example text.</message>
        </send_sms>
    </soap:Body>
</soap:Envelope>

The provider has published a PHP-script containing a class and function to easily access the API without having to deal with WSDL (I am rewriting that script into Rust).

But I see that in the PHP-script all the requests to the API are send in plain-HTTP. When I execute that script on my localhost and intercept it with Wireshark I can indeed see this part <password>MY_PASSWORD</password> of the request, exposing my password.

My question is: Is this a problem? When you have server-side PHP code running which calls an API, is it a problem if this is not over SSL?