At Least Your Landing Page Should Be JAMstack
I find there is very little argument for having your marketing site NOT be JAMstack. A Twitter friend of mine recently launched a side project he'd been laboring over for nine months on Product Hunt. Unbeknownst to him, it got to the top of HN a day later when he wasn't watching. HN brought in tens of thousands of hits and the site went down for hours... and my friend didn't know, because he thought his launch was done. Given a conservative estimate of 10K missed visitors and a 1% conversion rate, that is 100 users that were lost because the server went down. Not to forget negative impressions from existing users.
That's real money.
Of course, on managed platforms like Heroku, you can simply set auto restart and auto scale settings, but that will still cost. Better to just have a clean separation of www.mysweetproject.com and app.mysweetproject.com.
In particular, if your marketing site is JAMstack, launch days are far less stressful because your landing pages aren't vulnerable to being "hugged to death"; it keeps the top of your funnel open and only assigns compute resources to users that actually sign up. As a result of JAMstackifying, your marketing pages will probably also load faster, which matters for a first impression.
Whether or not the rest of your app is JAMstack is totally up to your tech preferences and product requirements; just remember that statically hosted assets don't mean static content, and the whole idea is that you can use as much or as little JS as you like, interacting with a decoupled API, to create the dynamic product experience you envision.