What I did was make Aurora Store my default app to open links, search for the desired app on my browser, and then long press and open with external application as explained (in more detail) on this reddit post.
Google bans new acounts that never used in official playstore before
Use a spare gmail acount that you have also used with playstore
Anonymus logins also get rate limits or get banned
As for alternative
App lounge from /e/ OS uses auroraOSS Gstore api to download from playstore so it's basically like using aurora
Other than that the are Python scripts you could use on termux but those also need a proper gmail account
Same apply to linux/windows programs available
I always used my "normal" google account in Aurora
also been using this account with microg since ages
Never had an issue
I don't care if the account gets banned though.