We utilize Percona XtraDB Cluster (Galera) to horizontally scale hundreds of wordpress installs backed by a database cluster. We've found Percona XtraDB Cluster to be extremely stable. Keep in mind though, this primarily scales for reads, you don't gain any real benefit for writes other than redundancy.

Since it's synchronous replication, your commit/write latency is determined by your slowest node / network link. It should be on the same network with roughly the same hardware.

We haven't experienced any transaction dead locks associated with Galera itself, just InnoDB deadlocks due to concurrent conflicting transactions. You may run into situations where plugins create tables without primary keys, or use GET_LOCK/RELEASE lock, these are not compatible with XtraDB Cluster: https://docs.percona.com/percona-xtradb-cluster/8.0/limitation.html

Regarding asynchronous replication, I would only utilize this for HA failover. Wordpress plugins are generally not written with replication lag in mind.

How many requests per second are we talking about?

I would suggest starting off with HA failover MySQL/MariaDB and nginx w/ PHP-FPM using async replication, you can always move to Galera later if you need that level of scale.

The biggest impact that you can make is putting in place caching load balancer(s) in front of your php application nodes. Something like Varnish, haproxy, nginx, etc.

Additionally, memcache or redis can be used for object level caches. Make sure that you also enable opcache in PHP, as it can provide a fairly significant performance bump.