All Intranet projects I deploy for customers I recommend to set their browser homepage as the Intranet. This aids adoption and engagement of the Intranet massively. You can do this for Edge and Chrome.
Some will even pop up the default browser on start-up of the desktops.
@has-dbk at the company where I am Intranet, SharePoint and Power Platform Manager, Internet Explorer/Edge is set via group policy to open the homepage whenever a user starts up their laptop or goes into the browser. We then have a policy that staff who use Chrome instead have it set as their homepage but they have to set that themselves.
Rob Los Gallardos Microsoft Power Automate Community Super User
You can add a "Frequent link" to the SharePoint start page but its below the fold of the page so no good in terms of using it the way into the Intranet from my experience.
The app icon good addition to the "hamburger" menu in the top left but you cannot deploy an app to the menu, each user has to find it and pin it which again doesnt work for a consistent navigation experience. I have deployed app icons and given instructions for users but the 20 odd intranet projects I have done have always set the default browser homepage.
HomeSites should be rolled out to all TR tenants by now I believe. Also if you have a a good DNS hosting provider you can easily have redirects. I just have Home.mydomain.com and intranet.mydomain.com redirect via dns redirect service that goes right to my page.
You can use spo-siteswap as well to move that site to your root if you do not use your root for anything else as well, or just a combination of these options.