NetNewsWire is a highly-acclaimed classic RSS reader for MacOS, iPhone and iPad.
Install: For MacOS, download and install the ZIP file from its website. For iPhone/iPad, go to the App Store and install it.
Add feeds: Provide the website URL that has the feed or the RSS/ATOM feed URL. By default, the feeds are downloaded and maintained locally on your device.
Sync: To sync between MacOS and iPhone/iPad, we need to use iCloud or the FreshRSS self-hosted feed aggregator. I found that the sync is super-slow through iCloud. For FreshRSS, provide the credentials and API URL as specified here. I think FreshRSS is the best option, since I can read my feeds on my iPhone, on my Macbook and also continue reading on my home Linux computer (through the self-hosted FreshRSS URL).