Architecture Question: How do you connect your landing page, pricing page and app?

Yes, same here.

One of the main reasons is that I want the marketing side server-side rendered, or static html, to speed up loading for SEO. The app can then be SSR or a SPA, but either way doesn't have to bother about SEO.

Another reason is that I want to be able to tweak / deploy the marketing site without having to bother app users (with potential downtime).

I've done the same thing as you ;)

I have the same identical setup. Though, now I'm trying to keep analytics for landing and app together so I can build a kind of funnel:

Visit Landing > Visit Sign Up > Sign Up > Actually use the app/Pay/Invite ...

I also have a SaaS where the landing page is both the marketing page and the app so I can showcase immediately the app to the user, but this makes sense as it is a small app (and I didn't want to develop another website :D)

Sounds decent

I think this is pretty difficult and so many people are working on some different platforms like jacobmartin you can visit here and use the easier way.

I keep everything under one app and use Next.js (minimal React framework) for SSR, code-splitting, and other benefits. I guess having a separate marketing site might make sense for larger teams, but I really like just easily being able to share styles and components across all pages.

I am deep into ssg (static site generators) and my approach would be different. Gatsby for example lets you build an spa inside your static site. You decide what the base route for your app will be and you create your spa like you would with a classic react app from there.
Honestly, I don't know if it is better. You have only one code base so it may simplify tooling, code reuse, design, ... And it may simplify analytics as well but I see many services doing as you do, even in the 'ssg world'.

Are these two separate applications? like I have my static marketing site www.mysaasapp.com build on Wordpress while my actual app app.mysaasapp.com is a JS based application running on Azure.
In any case, your marketing site can host multiple hooks to your app. I have a "more info" button on various pages that link two sites.
I have separate analytics for both sites so I can measure how the traffic is flowing between two sites.