There are typically two reasons for worrying about performance/load testing, either the team has trouble writing simple algorithms or specific performance requirements are part of an SLA. The third reason is that members of your team just like to worry about performance, aka Premature Optimization.
Performance tests should never be part of your unit testing. Unit tests are, by definition, for testing the correctness of the unit; Bubble Sort and Quick Sort are both valid implementations for a sorting requirement. Even if you have a performance requirement, that requirement will not be on the unit but on a vertical slice of the system. Assuming the bottleneck to be this unit is assuming too much. And if your unit tests take too long to run (ideally under one second, never more than 10) they become useless; developers start running them less frequently, not at all, or stop writing tests. Which leaves two options.
Make your performance tests part of your deployment pipeline. Performance tests are run after unit and integration tests as part of every commit (or whatever action triggers your pipeline). They will be run on your built artifact. Go this route if a SLA demands certain performance characteristics or if you're having trouble wrangling in your team's code quality ("Every time Jimmy makes a commit it brings the servers to their knees under heavy load and we spend days debugging the issue!").
Run your performance tests at night. Performance tests are scheduled to run at a certain time of the day. This is good for when your performance/load tests take a long time. Maybe you went the former route but these tests are becoming a bottleneck to releasing as frequently as you'd like. Now that you've gotten in the habit of running them more frequently maybe your team has gotten better at writing simple algorithms. Maybe now you can break your load tests apart into "tests that are absolutely required before we deploy to production" and "tests that keep us in good shape but problems with them don't surface that much".
It could be, as Doc Brown mentioned, that your performance tests take a week to run. But that's such an edge case I'll leave you to figure that one out when you get there. Report back here with your findings.
Running performance tests as part of your integration test phase doesn't feel right. Performance and load tests are generally used to track down problems with a vertical slice of your application so that you then have an indication of where to dive in. There wouldn't be much value to mocking out services as performance is a fickle beast. These services will respond differently under different loads. However, there could certainly be some 3rd party endpoint where they couldn't provide a sandbox for you. Maybe you can take production response time and stub them out appropriately. That response time could even be automated as new data comes in everyday.
There won't be a one size fits all and I suspect as you move forward you will come across a novel solution.