Actually, it does but they are shockingly unintuitive and hidden. The best way to change your preference among supported link handlers is to copy a URL, paste it into the notes app, then long press that link and choose “open with” either safari or your preferred app. That will stick until the next time you long press a link in this way.
An iOS developer for JIRA taught me this when I submitted feedback that the JIRA app suddenly stopped intercepting links (probably because I had inadvertently long-pressed to open a link in safari, not knowing I was setting a preference by doing so)
An iOS developer for JIRA taught me this when I submitted feedback that the JIRA app suddenly stopped intercepting links (probably because I had inadvertently long-pressed to open a link in safari, not knowing I was setting a preference by doing so)