[SalesForce] How to override Save button and show the popup in lightning-record-form of LWC

You should not really use standard__webPage.

Instead you can use standard__objectPage like below:

this[NavigationMixin.Navigate]({
        type: "standard__objectPage",
        attributes: {
            objectApiName: "Account",
            actionName: "new"
        },
        state: {
            nooverride: 1,
            useRecordTypeCheck: 1,
            navigationLocation: 'LIST_VIEW',
            backgroundContext: '/lightning/o/Account/list?filterName=00B280000047uEuEAI',
            recordTypeId: '0120K000000TO5KQAW'
        }
    });

You can get the filterName from using SOQL SELECT Id, Name, SobjectType FROM ListView WHERE SobjectType='Account'.

This will open the new record form (standard form) over list view. So, when its cancelled, directly mentioned list view is shown.

If you have 2 buttons you can create 2 JS methods to handle the buttons separately.

Your first method would simply save, your second method would call your first method and then manufacture the new record.

If you provide some sample code I can try to write a more detailed response. Please note, I wont write you a response that does 100% of the work for you.

Edit:

Based on the provided code sample, I think you need to read this documentation.

Overriding Default Behaviors

To customize the behavior of your form when it loads or when data is submitted, use the onload and onsubmit attributes to specify event handlers. If you capture the submit event and submit the form programmatically, use event.preventDefault() to cancel the default behavior of the event. This prevents a duplicate form submission.

<lightning-record-edit-form object-api-name="Seeded_Acre_Products__c" onsubmit={preventDefaults} > 
<lightning-button type="submit" variant="brand" label="Save" onclick={saveClick}>
</lightning-button>&nbsp;&nbsp; 
<lightning-button type="submit" variant="brand" label="Save & new" onclick={saveAndNewClick} value="saveandnew">
</lightning-button>

Javascript:

preventDefaults(event) {
    event.preventDefault(); 
    this.fields = event.detail.fields;
}

saveClick() {
    this.template.querySelector('lightning-record-edit-form').submit(this.fields);
}

saveAndNewClick() {
    saveClick();
    handleReset();
}

handleReset(event) {
   // Might be possible to use this.fields instead of a selector
   const inputFields = this.template.querySelectorAll(
       'lightning-input-field'
   );
   if (inputFields) {
       inputFields.forEach(field => {
           field.reset();
       });
   }
}