Clarification: The bug description should read
When inserting an HTML link (like <\a href="http://example.org">link title<\/a>)...

(backslashes added to prevent Mantis from formatting the example HTML)

What you enter in text fields is treated as text, and we just detect anything that looks like a URL and replace that with an anchor tag.

We do not parse HTML, so we do not have any notion of URL "title".

That cannot be quite correct, because the example.org link I posted in the bug description was a HTML link with link description, like this: <a href="http://example.org/">description</a>. You can edit this comment to see that it contains a HTML link with a description text that gets removed.

Only selected HTML tags are authorized within MantisBT text fields (see $g_html_valid_tags). Anchor is not one of them (to prevent a XSS attack vector).

When formatting text, we start by stripping all existing anchor tags (string_strip_href()), then encoding special chars, restoring authorized HTML tags, and finally adding links back (as plain URLs).

This is handled by the MantisCoreFormatting plugin [1]; you can disable URL processing entirely, or replace the core functionality by your own customized version of the plugin to handle anchors the way you want.

[1] https://github.com/mantisbt/mantisbt/blob/master/plugins/MantisCoreFormatting/MantisCoreFormatting.php#L95

Shouldn't this behaviour not kick in when adding the anchor element to $g_html_valid_tags, though? How would I circumvent this behaviour without having to modify the Mantis core, as that will get overwritten with every update?

Shouldn't this behaviour not kick in when adding the anchor element to
$g_html_valid_tags, though?

As mentioned previously, anchor tags are disabled to avoid security issues.
It is clearly mentioned in the doc NOT to add < a > to $g_html_valid_tags [1]

[1] https://github.com/mantisbt/mantisbt/blob/master/config_defaults_inc.php#L1797

How would I circumvent this behaviour without having to modify the Mantis
core, as that will get overwritten with every update?

This is exactly why I recommended you write a custom plugin to replace or supplement what MantisCoreFormatting does.