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👋eyy. I'd like to help you with your question. After taking a look to your solution there's a couple of things you can do to show the illustration.

• Adding a background-color and a background-image will make your styles collide, what can be causing problems to your container:

.container {
    // ❌ you should delete this property
    background-color: var(--white);
    background-image: url(/assets/images/illustration-sign-up-mobile.svg);
    background-repeat: no-repeat;
    background-size: contain;
    margin: 0 auto;
    max-width: 50rem;
    padding: 1.5625rem
}

• Your component does not have a container for your image:

  <main>
      <section class="container">
        <article class="signup-form">
          <h1>Stay updated!</h1>
          <p>Join 60,000+ product managers receiving monthly updates on:</p>
          <ul>
            <li><img src="./assets/images/icon-list.svg" alt="icon list">
              Product discovery and
              building what matters</li>
            <li><img src="./assets/images/icon-list.svg" alt="icon list">
              Measuring to ensure
              updates are a success</li>
            <li><img src="./assets/images/icon-list.svg" alt="icon list"> And
              much more!</li>
          </ul>
          <form action="success.html" id="newsletterForm" class="form">
            <label for="email">Email address</label>
            <input type="email" id="email" name="email"
              placeholder="[email protected]">
            <button type="submit" class="btn">Subscribe to monthly newsletter</button>
          </form>
        </article>
      </section>
    </main>

See, you did a great job using semantic html tags which makes me figured out the problem very quickly. You should create a container to store the image inside of it:

  <main>
      <section class="container">
        <article class="signup-form">
         // The rest of your code and the form goes in here
        </article>
         // Creates a container for your image
        <div class="image_container">
          <img src="./path/your-image.jpg" alt="your image"/>
        </div>
      </section>
    </main>

This way you can separate your component and make it easy for you to styled.

I hope this can help you fix your solution. Keep it up! you're doing a great job!