As @Erfan said Magento latest 2.3.4 isn't officially compatible with MySQL 8.
Although I can confirm that in our setup we have already upgraded to MySQL 8 from the first day of 2.3.4 released.
We don't have any errors in logs of magento or mysql logs.
Our setup was always using Percona server.
So we went again with this. We didn't installed magento 2.3.4 from scratch.
We just upgraded to 2.3.4 then we dumped the database from Percona 5.7
After we upgraded to Percona 8.0.18-9.
At last we imported the database to new Percona.
Before importing the database to Percona 8 we used some things of this Blog(@Erfan also mentioned it)
mysql> SET persist enforce_gtid_consistency=on;
mysql> SET persist_only gtid_mode=on;
This is just for future replication
mysql> SET PERSIST log_bin_trust_function_creators=1;
And this because sometimes magento database user need more privileges
Also you need to enable
Magento seems stable. Everything is working in admin and frontend without errors anywhere.
We also see some improvement in Magento's DB actions. It seems faster than Percona 5.7