Environment:
Browser / Version: Firefox Nightly 96.0a1 (🦎 96.0a1-20211108095312), Firefox Nightly 96.0a1 (2021-11-08)
Operating System: Google Pixel 5 (Android 11) - 1080 x 2340 pixels, 19.5:9 ratio (~432 ppi density), Samsung Galaxy S8 (Android 9) - 1440 x 2960 pixels, 18.5:9 ratio (~570 ppi density), Windows 10 Pro

Prerequisites:
Firefox Nightly browser opened in "Private" mode.

Steps to reproduce:

1. Navigate to https://brasil.estadao.com.br/noticias/geral,mpf-cobrou-em-junho-anac-apuracao-de-denuncia-sobre-aviao-que-caiu-com-marilia-mendonca,70003890777?utm_source=twitter:newsfeed&utm_medium=social-organic&utm_campaign=redes-sociais:112021:e&utm_content=:::&utm_term=
2. Observe the page.

Expected Behavior:
The page loads without asking for login to see the content.

Actual Behavior:
A notification message is displayed, asking for login in order to access the page content.

Notes:

1. Screenshot attached.
2. The issue is not reproducible with normal mode.
3. The issue is also reproducible on Firefox Nightly desktop - Private mode, but it is not reproducible on Chrome desktop - Incognito mode.

This appears to be a paywall script. I'm not asked for a login in strict mode, so it's almost certainly caused by the script checking if serviceworkers/indexeddb are available to detect private browsing mode. Sure enough, in their gtm.js they're looking for both, as well as localStorage:

this.detectBrowsingMode = function(b) {
    navigator.serviceWorker ?
        this.BrowsingModeDetector.setBrowsingInNormalMode() :
        this.BrowsingModeDetector.setBrowsingInIncognitoMode();
// etc

We might be able to provide a site-specific intervention until bug 1320796 is resolved.

I no longer see that message on their site, or the source code which showed it, or any obvious signs that they're relying on any web APIs that aren't available in private browsing mode.

Oana, can you confirm if it also no longer shows that message for you now? If so, we can close this.

Indeed, the message is no longer displayed.
https://prnt.sc/OwEn7BxaOsZh

Tested with:
Browser / Version: Firefox Nightly 103.0a1 (2022-06-16)
Operating System: Windows 10 Pro