Accessing JSON fields in html of LWC

That is because HTML will load before your external call finishes and Profile will be undefined before getting response and so I would suggest to use conditional rendering in HTML itself so that you can fetch the values directly instead of increasing Javascript code for implementing multiple getters.

HTML:

<template>
    <template if:true={profile}>
        {profile.Name.First}
        {profile.Name.Last}
        {profile.Email}
        {profile.Phone}
    </template>
</template>

As you see, there is no need of implementing 4 getters in JS

Change your template to use a getter that checks for null down the object tree

in JS

get name(){
let returnValue = '';

if(this.profile && this.profile.Name && this.profile.Name.First){
  returnValue = this.profile.Name.First;
}
return returnValue;
}

in html

<template>
    {name}
</template>

What's happening is you are looking for the name on profile before the browser has had a chance to make the call to the service so there is no name to get yet.

Reference: https://wipdeveloper.com/lwc-getting-data-with-the-wire-service/