GetCurrentUser ($().SPServices.SPGetCurrentUser) in peoplepicker (JQuery), using Content Editor add NewForm.aspx.

<script type="text/javascript" src="/sites/test/SiteAssets/jquery-2.1.3.min.js"></script>
<script type="text/javascript" src="/sites/test/SiteAssets/jquery.SPServices-2014.02.min.js"></script>
<script src="/_layouts/15/clientpeoplepicker.js" type="text/javascript"></script>

    (function () {
        var ctx = {};
        ctx.Templates = {};
        ctx.Templates.Fields = {
            'Applicant': {
                'NewForm': renderAssignedTo
            }
        };
        SPClientTemplates.TemplateManager.RegisterTemplateOverrides(ctx);
    })();
    
    function renderAssignedTo(ctx) {
         var currentUser = $().SPServices.SPGetCurrentUser({fieldNames: ["Title", "Name"]});
         var currentUserEntry = createUserEntity(currentUser.Name,currentUser.Title);
         //Set user default value
         ctx.CurrentFieldValue = [];   
         ctx.CurrentFieldValue.push(currentUserEntry);  
         return SPClientPeoplePickerCSRTemplate(ctx);
    }
    
    function createUserEntity(userLoginName,userDisplayName)
    {
       return {
          Description: userLoginName,
          DisplayText: userDisplayName,
          EntityGroupName: "",
          EntityType: "",
          HierarchyIdentifier: null,
          IsResolved: true,
          Key: userLoginName,
          MultipleMatches: [],
          ProviderDisplayName: "",
          ProviderName: ""
       };
    }

make a SharePoint FormApp (via Integrate > Power Apps > Customize Forms). If the form is a canvas app, you can modify easily the default values of the fields.

Whether you use SharePoint server or SharePoint online?

For SharePoint server, add a content editor web part in the New form, then use following codes in the content editor web part.

<script src="https://code.jquery.com/jquery-1.10.1.min.js"></script> 
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jquery.SPServices/0.7.1a/jquery.SPServices-0.7.1a.min.js"></script>
 
<script type="text/javascript">
 $(document).ready(function() {
     var user= $().SPServices.SPGetCurrentUser();    
      $("div[title='People Picker']").text(user);
  });
</script>

For SharePoint online, refer this article to auto populate logged In username in the PowerApps form.