Great questions, and so glad to hear you got that working!
Regarding Option 1 - I believe you are missing the redirect at present because you are logged in. If you log out, the redirect will start happening again. Connect is trying to balance two things for you: As a logged in user, you have the ability to make changes to applications / publish new ones / etc. That is done in the dashboard.
As a not-logged-in user, the landing page (served at /connect/) will redirect where you want it to - in this case an App. If you have thoughts on how you envision this dichotomy and what would work better for you, we are definitely all ears!
On option 2:
That is right - if you are using version 1.8.0, then that is the right version of the documentation
For the latest version of the docs, you probably want this one: https://docs.rstudio.com/connect/admin/proxy/#simple-configuration
To be clear, though, you probably don't need the full "path-rewriting configuration." That is only needed if you are hosting Connect itself at a path other than root. I.e. at /rsc/, so your app URL would be /rsc/my-app/. The X-RSC-Request is not "standard" per se, but it is just a special header being added to tell Connect about what the proxy is doing
For non-path-rewriting configuration, it is superfluous and can be substituted for more standard X-Forwarded-* headers if that is preferable.
In any case, I suspect you would only need a line like this to take our simple configuration into what you're looking for. It's worth keeping in mind that nginx is another service and another potential point of failure being introduced into your infrastructure. For instance, we have seen cases where a proxy in front of the product blocks upload bundles of a certain size (mitigated by client_max_body_size 1024m; or some such), or times out websocket connections after a certain time (mitigated by things like proxy_read_timeout 20d;), etc. It's also worth documenting why nginx is a part of your infrastructure in case you are ever inclined to remove it! (It can be hard to remove things when you don't remember why they are there... spoken from experience
)
In any case, this is a simple (untested) redirect that might provide a starting point:
rewrite ^/$ https://$http_host/myapp/ permanent;