Is there a way to preserve linebreaks in nodes without typing <br>?

To what purpose?

You've used <code> properly in your OP and I don't see anything in this thread that can't be attributed to individual style where <br> would be needed unless it's the parent of this post, where (personal style, again), I might have broken up your monolithic text into paragraphs, using <p>... </p> pairs.

For more general advice on formatting your nodes, check Writeup Formatting Tips and because it's comprehensive, follow, near the bottom, the link to Perl Monks Approved HTML tags.

And lest we forget, your browser's "View Source" may add some answers, if you see some kind of fancy formatting not readily attributable to breaks, paragraphs, or (not previously mentioned) lists whether ordered or unordered.

Just BTW, there are no <br>s in the source of this entry.