It's absolutely substantiated. I can easily reproduce the phenomenon myself using curl from the command line. The key is to use a web browser User-Agent (curl -A), because it doesn't happen for curl's own User-Agent. The delay is consistent and only affects certain Musk-hated domains such as the NYT and Threads. Here's an example, try it yourself:
curl -v -A 'Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/605.1.15 (KHTML, like Gecko) Version/16.6 Safari/605.1.15' https://t.co/d8KWBqT5v6