Remove from

try this

add_filter( 'the_content', 'remove_paragraphs_inside_blockquotes', 9  );

function remove_paragraphs_inside_blockquotes( $content ) {
    $dom = new DOMDocument();

    libxml_use_internal_errors(true);
    $dom->loadHTML('<?xml encoding="utf-8" ?>' . $content, LIBXML_HTML_NODEFDTD | LIBXML_HTML_NOIMPLIED);
    libxml_clear_errors();

    $blockquotes = $dom->getElementsByTagName('blockquote');
    
    foreach ( $blockquotes as $blockquote ) {

        foreach ( $blockquote->childNodes as $child ) {
            if ( $child->nodeName === 'p' ) {
                while ( $child->firstChild ) {
                    $blockquote->insertBefore($child->firstChild, $child);
                }
                $blockquote->removeChild($child);
            }
        }
    }

    $content = $dom->saveHTML();

    return $content;
}

for display

<?php echo apply_filters( 'the_content', wp_kses_post( get_the_content() ) ); ?>