I design my current web apps to work using serverless functions https://serverless.com/ This ensures that if my applications become popular, I will not have to do additional infrastructure work to scale. I use a cloud provider managed database (AWS DynamoDB, RDS for Postgresql) so I don't need to worry about managing that either.
There is a steep learning curve! A quick Google search shows that Rust serverless is in its infancy (https://github.com/softprops/serverless-rust). Also, if you need to have bi-directional communication using WebSockets (or something comparable), the options you have to work with are limited (AWS AppSync is what I am currently struggling with)
That being said, it has been an extremely challenging and rewarding experience, migrating my personal projects.