Back to the archive page, I figured it out, leaving this here as a note to others and future me perhaps 
First, I found layouts/_default/list.archivehtml.html
and made a slight change (<p>is this thing on?</p>
sort of thing) and I did not see changes in the archive page. I’m no Hugo expert, but the code also seemed too short and did not match what I saw in front of me for my Archive page, which includes categories at the top.
Then going through the template files, I realized TinyTheme, which I use, has its own archive page which is listed in the TinyTheme section under design. The code there matched what I was seeing in my archive page, obviously… duh. OK, so changes should come there.
But… even better:
Matt figured out people would like to explain their archive page a bit further, and added a microhook for archives (New - Tiny Theme 2.0 with Microhooks) which means that if all I want is to add something before the archive, I can use the hook instead as explained in the documentation. I could even throw in the new blogroll shortcode after that. (this doesn’t seem to work, actually)
Now, if on top of that I want to add certain style just for that page, I can go into TinyTheme’s layouts/_default/list.archivehtml.html
and include <style>
tags as long as they are after the {{ define "main" }}
.
Also, if through the process you somehow manage to delete TinyTheme’s default Archive page (not that it happened to me, no no, not at all) you can get it from github. I’d think Microblog restores the default, and maybe it does, but in this case, we’re not using the default but TinyTheme’s, so it’s either copy-paste from Git Hub or re-install the plugin, I think.