If a long-press on an Instagram caption does nothing useful, the app is doing that on purpose. Captions on Reels and many posts are not a normal text field. Selection, share-as-text, and copy are limited inside Instagram.
What is blocked
You can usually read the caption, expand it, and tap a hashtag. You often cannot drag a cursor through the sentence. Screenshots do not give you editable text. Logging in as someone else is not a fix, and Caption Copy never asks for an Instagram login.
What still works
A public post still has a link. That link is enough to request the caption as plain text. Private posts stay private. Deleted posts fail with a clear message.
What to do next
Copy the link from Share, then open Instagram caption copy. Paste, get the caption, and copy the text or only the hashtags. The Android app can save that caption after you copy it, and it can also be opened from Instagram's share sheet.