I disable both. Keep in mind, sometimes Play Store respawns itself (goes from disabled to enabled all on its own) and starts the process over again.
I also couple disabling both Play Store and Download Manager by also side-loading an app called Netguard No-Root Firewall. That app can be found on APKPURE, and after you enable 'unknown sources' in security settings, you should be able to download that file on any browser (preferably one with its own download manager like Samsung Internet which works on any phone, or Firefox) and then use your file explorer app to select the file, and tap it. You should get an install prompt, and then tap done when you see 'app installed'
Then open NetGuard, and go to settings, advanced, and enable 'system apps' then go back and find Play Store, Download Manager and make sure both the wifi and data symbol has a slash through them. Also, since this is a phone app we're talking about here, you can also disable the wifi/data for Phone by Google as well, and then it should not only never update again, but just work as a regular old phone dialer.