The problem is that it's very hard to distinguish between "posts with links get less engagement because Twitter is subtly suppressing them" and "posts with links get less engagement because people are just less likely to click 'like' and 'retweet' on them."

I might be wrong, but IIRC, the 'links dont get clicked' was already a problem before they started adding algorithms to the timeline. This is about clicks and not engagement though.

Also, you can see how many times a tweet was viewed and interacted with in the analytics, so you could try to do your own comparison by seeing the % of views that trigger engagement