Making the logo bigger

Even with a vector-based SVG logo, this font (the smaller one in your logo) would no longer be legible.

You could make the header area larger overall, but then let it shrink so it doesn’t take up too much space.

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Another option would be to display the logo larger at first and then have it move to the desired position inside navigation as the page is scrolled.
this for child-theme functions.php:

function logo_shrink_navigation(){
?>
<script type="text/javascript">
(function($) {
    function initLogoScrollAnimation() {
        // ===== CONFIGURATION =====
        var config = {
            maxScroll: 100,
            scaleStart: 2.3,
            scaleEnd: 1,
            translateYStart: 80,    // Starting point shifted in the Y direction (e.g. 80px for down shift)
            translateYEnd: 0,       // End point (must be 0 for the final position)
            translateXStart: -230,  // Starting point shifted in the X direction (e.g. -100px for the left)
            translateXEnd: 0        // End point (must be 0 for the final position)
        };
        // =========================
        
        var ticking = false;
        var $menuLogo = $('#menu-item-logo');
        var $menuLogoLink = $menuLogo.find('a');
        var $menuLogoImg = $menuLogo.find('img');
        var logoWidth;
        
        function updateLogo(scrollTop) {
            var progress = Math.min(scrollTop / config.maxScroll, 1);
            
            // Skalierung berechnen
            var scaleDiff = config.scaleStart - config.scaleEnd;
            var scale = config.scaleStart - (scaleDiff * progress);
            
            // Y-Verschiebung berechnen
            var translateYDiff = config.translateYStart - config.translateYEnd;
            var translateY = config.translateYStart - (translateYDiff * progress);

            // X-Verschiebung berechnen (NEU)
            var translateXDiff = config.translateXStart - config.translateXEnd;
            var translateX = config.translateXStart - (translateXDiff * progress);
            
            var extraSpace = (scale - 1) * logoWidth / 4;
            
            // Transform mit translateX ergänzt
            $menuLogoLink.css('transform', 'translateX(' + translateX + 'px) scale(' + scale + ') translateY(' + translateY + 'px)');
            
            $menuLogo.css({
                'margin-left': -extraSpace + 'px',
                'margin-right': -extraSpace + 'px',
                'z-index' : '19'
            });

            $menuLogoImg.css({
                'background-color': 'rgba(255,255,255,0.8)',
                'backdrop-filter': 'blur(5px)',
                'border-radius': '25px',
                'border': '1px solid #FFF'
            });
        }
        
        $(window).on('scroll', function() {
            var scrollTop = $(window).scrollTop();
            
            if (!ticking) {
                window.requestAnimationFrame(function() {
                    updateLogo(scrollTop);
                    ticking = false;
                });
                ticking = true;
            }
        });
        
        // Logo-Breite messen und initial setzen
        logoWidth = $menuLogoLink.outerWidth();
        updateLogo($(window).scrollTop()); // Initialen Scrollwert beim Laden berücksichtigen
    }
    
    $(document).ready(function() {      
        setTimeout(function() {
            initLogoScrollAnimation();
        }, 300);
    });  
})(jQuery);

</script>
<?php
}
add_action('wp_footer', 'logo_shrink_navigation');

the confic section is for the starting look of your logo (scale, shift x and y-axis etc)

look at start this way:

after scroll it is in the center of your nav.