HypnoSloth Can you get away with using only aurora without any or all of the sandboxed google play apps?
Depends on the apps. Some apps absolutely require the presence of google components. More explanation below.
HypnoSloth I assume push notifications wont work and some apps may not function properly but is it a hard dependency for all apps?
No, not at all. Each app is different, its really a case by case here. a lot of apps don't need notifications at all and can even be blocked from the internet completely, even if they are from play store. You can even install apps that have ads and trackers, like a chess game, and block it from the internet permanently (assuming it still works, many do). You can even update the app without it ever regaining access to the internet. Apps that need push notifications are generally mostly chat/communication apps (signal, whatsapp, facebook, etc), and some "internet service" like email. But even then I don't always "need" the notification and the app still works. For example I don't need to know that I have an email "right now" for example. I can just check it manually when I want to. So it really depends on the app.
However some apps simply refuse to open without the presence of GSF or play services. Like perhaps facebook, or doordash, or maybe slack. In these cases if you want the app, you will have to install play services and in some cases both the app and play components can be internet blocked and in other cases one or both have to have internet access. So with uber for example you might have to give internet access to both. But profiles could help a bit here here to reduce data exposure.
An app like Slack is very likely a privacy invasive app; not to the extent of facebook, but still. And likely you need to be internet connected and "need" notifications for sure as my guess is that you likely need it for communication with colleagues and need to respond with immediacy. In such a case, depending on how much you use it, installing on a second profile might be a bit of a hassle (if you use it constantly), but might also be ok and might solve your issue. Worst case is you install all on the same profile.
The main problem here is that if Slack has your "Identity" then that Identity will be connected to the installed instance of google services of the current profile. This instance has access to your IP address and slack, but beyond that it doesn't know much else about your phone, unless you have installed other "google co-operating" apps in the same profile, in which case they'll share data (I think).
The best way to deal with this is to write a list of all the "privacy problematic" apps that you "have to have" and build your strategy around that. You may be able to get away with creating one or two extra profiles and that might solve your problem. And then you can try to utilize foss apps for your other needs.
Lastly the question "Can you get away with using only aurora apps" , I think this might have been a question. Answer is yes but again depends on the app. For example a particular banking app might not work if its not strictly locked to an exclusive google account (detects account sharing and refuses to work).
Also some great apps are not available in play store at all (NewPipe, Bromite, adblockers), so you'd still benefit from diversifying your sources. My previous post explained that.