how do i fix broken internal links properly?

Crawl the site first - Screaming Frog's free version does up to 500 URLs - and export the 404s along with their inlinks, so you know which page each broken link sits on. Then fix it at the source: edit the link to point at the right live URL. Don't just 301 the dead URL and leave your own links pointing at it. The redirect is the backup for outside links you can't edit, not the fix for links you control. If the page is gone for good with no replacement, remove the link and leave the anchor as plain text.