You can also use the other simple way by embedding icon in the lightning-button

<lightning-button variant="success" label="Next" title="Next" icon-name="utility:forward" icon-position="right" class="slds-m-left_x-small"></lightning-button>

More information : https://developer.salesforce.com/docs/component-library/bundle/lightning-button/example

You can also use the other simple way by embedding icon in the lightning-button

<lightning-button variant="success" label="Next" title="Next" icon-name="utility:forward" icon-position="right" class="slds-m-left_x-small"></lightning-button>

More information : https://developer.salesforce.com/docs/component-library/bundle/lightning-button/example

                                 OR

In your case : Use variant="bare-inverse" in lightning-button-icon

<button class="slds-button slds-button_neutral" style=" border: none;background-color: #04844B;color: white;">Next
<lightning-button-icon icon-name="utility:forward"  variant="bare-inverse" alternative-text="Settings" title="Settings"></lightning-button-icon>
</button>