Deal with potential problems in a logical order, avoiding the temptation to prematurely optimise.
Write your microservice application to be scalable. The most important part of this is that it is stateless. You should be able to spin up / shut down individual instances of the service without issue.
If you ever need to scale up your applicationservice due to demand, your code is not a blocker, and it should be relatively straight forward.
If you need shared state between containersservice instances, use a shared cache, such as Redis.
Scaling your database is a different issue. It makes sense in 90% of cases to have a single database that all copies of your applicationservice to connect to, until your load causes problems.
Horizontally scaling databases do exist (or correctly utilising a no-SQL db such as Cosmos, if you can properly design around the partition keys), but they tend to be more complex and expensive.
Other options do exist if you reach this point. E.g. would you start to have a database per tenant, per service, instead of a single database for all?