[me.bluemail.mail] can't add Gmail account

Affected app
Name: BlueMail
Package id: me.bluemail.mail

Describe the bug
When adding Google account to BlueMail, I think it is supposed to show a Google loging screen, because it kinda tries to redirect to a new screen, but immediately go back to BlueMail without showing anything

To Reproduce
Steps to reproduce the behavior:

1. Go to BlueMail
2. If it's not installed, try to add a Google account during initial setup, else, try to add one using the three dots, bottom left
3. Type your gmail adress. Bluemail will try to force you into a Google screen connexion but will fail.

Expected behavior
I don't remember how it works on a normal phone, but it used to work on my stock rom with normal Google play services
Currently using lineageOs

Screenshots
I can take a video if you want? A screen shot won't help
https://drive.google.com/file/d/1m4gXTxc6BVVPSi4KDF8lIm5-futl7MF8/view?usp=sharing

System
Android Version: 13
Custom ROM: Lineage Os 20-20230706-microG-haydn

microG
microG Core version: 0.2.27.223616
microG Self-Check results: All ticked

Start by reproducing the account-add flow in BlueMail on Android 13 with LineageOS 20 and microG Core 0.2.27.223616, using the provided reproduction steps and video. Compare the redirect behavior with the expected Google login flow; done means the Google screen appears and a Gmail account can be added.