specificlee Let's say I use a phone with a traditional sim card that is linked to my IRL identity on the Owner profile. If I limit traditional phone usage and SMS to this main profile, am I still "giving away" any information about my usage on on other user profiles where I only use data via VPN?
You are giving away which country the SIM card is connected in. But this is usually not much of a problem, as which country you reside in is not a very precise location of where you are, nor does it reveal anything about who you are. You are probably leaking that anyway through configured timezone and system language.
Apps in the other user profile should not be able to see your phone number or any other unique identifier of your SIM card, nor should they be able to see any of your phone or SMS activity at all, as long as you have properly disabled telephony and SMS for that user profile in Settings app -> System -> Users -> Your user account.
specificlee My understanding is that absent some way to unlink your SIM card from your IRL identity (which is not really practical in my case), the best way to protect your privacy re: traditional cell services like talk and SMS is to not use them. However, if I use my SIM card only for data, and I use a VPN, what information if any is my device giving away? Does it matter which profile I am using?
You would be giving away the same information as if you were connected to a Wifi access point, using a VPN. Your internet service provider will know who you are and where you are, and that you are using a VPN, and which VPN specifically. But other than that, they will only see encrypted VPN traffic. Your VPN service provider will know both who you are, where you are and what you are doing, they will know everything about you. But they promise to not save any logs about that. Websites and services you use will not know your location nor who you are, unless you or any of your apps tell them about this. (Pro-tip, disable all network location services in the phone settings.)
So, using cellular data traffic instead of Wifi is not really changing anything.
specificlee Let's say I download apps on the main "Owner" profile but then use the "install available apps" in specific user profiles. Is there any risk of having many apps installed on the "Owner" profile, even if I only use these apps on the specific User profiles? For example, if I download Signal, Firefox, and YouTube on the main user profile, but use "install available apps" to install each one on a separate user profile, does it matter that I still have all three apps downloaded on the "Owner" profile?
You can disable the apps in the owner profile if you want, in Settings app -> Apps -> The app -> Click "Disable". The apps will still be enabled and working on other user profiles, and should still be updatable as usual in the owner profile, but won't run in the owner profile at all.
specificlee Does the fact that I am using the "install available apps" feature undermine the isolation of each user profile?
No. All apps are globally installed on your phone and shared between all user profiles anyway. Only app data is specific for each user profile. So app version and exact time at which the app was installed will be accessible and the same across all profiles, whether you install them using "Install available apps" or by installing them from an app store inside each respective profile.
specificlee I would like to see notifications from my apps across user profiles. However, I note that, for example, Signal is not giving me pop up notifications. Is that normal? Do I need to download or install something else?
No idea.