Mastodon.social links behave differently than other links on Threads:

All links posted to Threads have a tracking parameter attached to the URL, and will open to the in-app browser when clicked. This includes third party server links.

mastodon.social profile links seem to be an exception. links from this specific server, open in the native Mastodon app and tracking parameters appear to be omitted.

My omg.lol server link after posting to threads but before clicking on it: