Probably, but /etc/hosts
just fixes DNS resolution issues. From your curl example, the host is already resolving to that IP:
curl https://downloads.wordpress.org/plugin/ultimate-addons-for-gutenberg.1.25.4.zip -vvv
* Trying 198.143.164.250:443...
So adding 198.143.164.250 downloads.wordpress.org
to your hosts file just seems redundant, but I suppose it’s worth a try
I’d ignore doing things the “trellis way” for now and just manually modify /etc/hosts
to see if it helps.
I’m not sure how much more help I can offer beyond this, but if possible I’d just re-create a new staging server and see if that fixes it.